2

I'm trying to get 3 really long equations (that I've split) to be aligned more elegantly with their respective equal signs in some way. Shortening the LHS of those 3 equalities (perhaps splitting it 3 times?) would help align the full derivation more in the center of the page as well. I defer to the tastes of others on what "more elegantly" means.

enter image description here

I tried the methods discussed here and in attached questions but to no avail One multiline equation and many single line equations inside align environment

\begin{align} 
0&= 0+0+0 \\ \notag
0 &=   R_{\mu\nu}{}^a e_{\rho a} + R_{\rho\mu}{}^a e_{\nu a} -R_{\nu\rho}{}^a e_{\mu a} \\ \notag
R_{\nu\rho}{}^a e_{\mu a} &=   R_{\mu\nu}{}^a e_{\rho a} + R_{\rho\mu}{}^a e_{\nu a}  \\ \notag
(\partial_{[\nu} e_{\rho]}{}^a - \omega_{[\nu}{}^{ab} e_{\rho]}{}_b) e_{\mu a} &=   (\partial_{[\mu} e_{\nu]}{}^a - \omega_{[\mu}{}^{ab} e_{\nu]}{}_b) e_{\rho a} + (\partial_{[\rho} e_{\mu]}{}^a - \omega_{[\rho}{}^{ab} e_{\mu]}{}_b) e_{\nu a}  \\ \notag
\partial_{[\nu} e_{\rho]}{}^a e_{\mu a} - \omega_{[\nu}{}^{ab} e_{\rho]}{}_b e_{\mu a}&=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} - \omega_{[\mu}{}^{ab} e_{\nu]}{}_b e_{\rho a} + \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - \omega_{[\rho}{}^{ab} e_{\mu]}{}_b e_{\nu a}   \\ \notag
\omega_{[\mu}{}^{ab} e_{\nu]}{}{}_b e_{\rho a} + \omega_{[\rho}{}^{ab} e_{\mu]}{}_b e_{\nu a} - \omega_{[\nu}{}^{ab} e_{\rho]}{}_b e_{\mu a} &=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  + \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} \\ \notag 
\frac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} - \frac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a}  +\frac{1}{2} \omega_{\rho}{}^{ab} e_{\mu}{}_b e_{\nu a} \\ \notag -\frac{1}{2}\omega_{\mu}{}^{ab} e_{\rho}{}_b e_{\nu a}- \frac{1}{2}\omega_{\nu}{}^{ab} e_{\rho}{}_b e_{\mu a} +\frac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a}&=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  + \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\ \notag 
\bigg(\frac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} -\frac{1}{2}\omega_{\mu}{}^{ba} e_{\rho}{}_a e_{\nu b}\bigg) + \bigg( \frac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} \\ \notag + \frac{1}{2} \omega_{\rho}{}^{ba} e_{\mu}{}_a e_{\nu b}\bigg)+ \bigg(-\frac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a}  - \frac{1}{2}\omega_{\nu}{}^{ba} e_{\rho}{}_a e_{\mu b}\bigg) &=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  + \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\ \notag 
\bigg(\frac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} +\frac{1}{2}\omega_{\mu}{}^{ab} e_{\rho}{}_a e_{\nu b}\bigg) + \bigg( \frac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} \\ \notag - \frac{1}{2} \omega_{\rho}{}^{ab} e_{\mu}{}_a e_{\nu b}\bigg)+ \bigg(-\frac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a}  + \frac{1}{2}\omega_{\nu}{}^{ab} e_{\rho}{}_a e_{\mu b}\bigg) &=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  + \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\ \notag 
\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a}  + 0 + 0 &=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  + \partial_{[\rho} e_{\mu]}{}^c e_{\nu c} - \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} 
\\ \notag 
\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} e^{\rho a} e^{\nu b}&=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}e^{\rho a} e^{\nu b}  + \partial_{[\rho} e_{\mu]}{}^c e_{\nu c}e^{\rho a} e^{\nu b} - \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\ \notag 
\omega_{\mu}{}^{ab} &=   \partial_{[\mu} e_{\nu]}{}^a  e^{\nu b}  + \partial_{[\rho} e_{\mu]}{}^c \delta_c^b e^{\rho a} - \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\ \notag 
\omega_{\mu}{}^{ab} &=   \partial_{[\mu} e_{\nu]}{}^a  e^{\nu b}  + \partial_{[\rho} e_{\mu]}{}^b e^{\rho a} - \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\ \notag 
\omega_{\mu}{}^{ab} &=   e^{\nu b}\partial_{[\mu} e_{\nu]}{}^a    + e^{\nu a}\partial_{[\nu} e_{\mu]}{}^b  -e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\lambda} e_{\rho]}{}^c
\\ \notag 
\omega_{\mu}{}^{ab} &=   2 e^{\nu [b}\partial_{[\mu} e_{\nu]}{}^{a]}    +e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\rho} e_{\lambda]}{}^c
\\ \notag 
\omega_{\mu}{}^{ab} &=   -2 e^{\nu [a}\partial_{[\mu} e_{\nu]}{}^{b]}    + e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\rho} e_{\lambda]}{}^c
\end{align}

My first instinct was to use aligned, but I am not sure how to accomplish this

Can anyone provide some help in making the 3 multiline (very long if not) equalities in my above code prettier?

4
  • 1
    Plese provide a proper MWE. There are 12 equations. You mean the 3 in the middle? And what do you mean with 'prettier'? – Steradiant Jun 10 '20 at 16:40
  • indeed the 3 long ones in the middle. I will include some additional info in the question – Lopey Tall Jun 10 '20 at 17:00
  • 1
    What do you mean with 'prettier'? Prettiness is very subjective – Steradiant Jun 10 '20 at 17:07
  • To be honest, I'd opt for left alignment overall. – egreg Jun 11 '20 at 15:16
3

Some suggestions:

  • Omit all \bigg sizing directives and omit the associated opening and closing parentheses.

  • Break the left-hand parts of the three long equations into three rather just two parts and use \qquad and \quad directives to "shove" the first and second lines to the left and create a slightly staggered look.

  • Use \tfrac{1}{2} rather than \frac{1}{2} throughout.

  • Add a bit of whitespace before and after the group of three 3-line equations.

  • Don't place huge amounts of material (such as long-ish math expressions) on any given line. That way, line information given in error messages will help speed up the debugging procedures, since there's less on any given line that can go wrong.

enter image description here

\documentclass{article}
\usepackage[margin=2.5cm]{geometry} % set page size parameters suitably
\usepackage{amsmath}
\allowdisplaybreaks
\begin{document} 
\begin{align*} 
0 &= 0+0+0 \refstepcounter{equation} \tag{\theequation}
\\
0 &= R_{\mu\nu}{}^a  e_{\rho a} + 
     R_{\rho\mu}{}^a e_{\nu a} -
     R_{\nu\rho}{}^a e_{\mu a} 
\\ 
R_{\nu\rho}{}^a e_{\mu a} 
&= R_{\mu\nu}{}^a e_{\rho a} + R_{\rho\mu}{}^a e_{\nu a} 
\\ 
(\partial_{[\nu} e_{\rho]}{}^a - 
 \omega_{[\nu}{}^{ab} e_{\rho]}{}_b) e_{\mu a} 
&= (\partial_{[\mu} e_{\nu]}{}^a - 
    \omega_{[\mu}{}^{ab} e_{\nu]}{}_b) e_{\rho a} + 
   (\partial_{[\rho} e_{\mu]}{}^a - 
    \omega_{[\rho}{}^{ab} e_{\mu]}{}_b) e_{\nu a} 
\\ 
\partial_{[\nu} e_{\rho]}{}^a e_{\mu a} - 
\omega_{[\nu}{}^{ab} e_{\rho]}{}_b e_{\mu a}
&= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} - 
   \omega_{[\mu}{}^{ab} e_{\nu]}{}_b e_{\rho a} + 
   \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - 
   \omega_{[\rho}{}^{ab} e_{\mu]}{}_b e_{\nu a} 
\\ 
\omega_{[\mu}{}^{ab} e_{\nu]}{}{}_b e_{\rho a} + 
\omega_{[\rho}{}^{ab} e_{\mu]}{}_b e_{\nu a} - 
\omega_{[\nu}{}^{ab} e_{\rho]}{}_b e_{\mu a} 
&= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} + 
   \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - 
   \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\[1ex]
\tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} -
\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a}  \qquad& \\
{}+\tfrac{1}{2} \omega_{\rho}{}^{ab} e_{\mu}{}_b e_{\nu a}  
  -\tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\rho}{}_b e_{\nu a} \quad& \\
{}-\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\rho}{}_b e_{\mu a}
  +\tfrac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} 
&= \partial_{[\mu}  e_{\nu]}{}^a  e_{\rho a} + 
   \partial_{[\rho} e_{\mu]}{}^a  e_{\nu a} - 
   \partial_{[\nu}  e_{\rho]}{}^a e_{\mu a} 
\\ 
\tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} -
\tfrac{1}{2}\omega_{\mu}{}^{ba} e_{\rho}{}_a e_{\nu b}     \qquad& \\ 
{}+\tfrac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} 
  +\tfrac{1}{2} \omega_{\rho}{}^{ba} e_{\mu}{}_a e_{\nu b} \quad& \\
{}-\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a} 
  -\tfrac{1}{2}\omega_{\nu}{}^{ba} e_{\rho}{}_a e_{\mu b} 
&= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} + 
   \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - 
   \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\ 
\tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} +
\tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\rho}{}_a e_{\nu b}     \qquad& \\ 
{}+\tfrac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} 
  -\tfrac{1}{2} \omega_{\rho}{}^{ab} e_{\mu}{}_a e_{\nu b} \quad& \\
{}-\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a} 
  +\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\rho}{}_a e_{\mu b} 
&= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} + 
   \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} - 
   \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\[1ex]
\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} + 0 + 0 
&= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} + 
   \partial_{[\rho} e_{\mu]}{}^c e_{\nu c} - 
   \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} 
\\ 
\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} e^{\rho a} e^{\nu b}
&= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}e^{\rho a} e^{\nu b} + 
   \partial_{[\rho} e_{\mu]}{}^c e_{\nu c}e^{\rho a} e^{\nu b} - 
   \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\ 
\omega_{\mu}{}^{ab} 
&= \partial_{[\mu} e_{\nu]}{}^a e^{\nu b} + 
   \partial_{[\rho} e_{\mu]}{}^c \delta_c^b e^{\rho a} - 
   \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\ 
\omega_{\mu}{}^{ab} 
&= \partial_{[\mu} e_{\nu]}{}^a e^{\nu b} +   
   \partial_{[\rho} e_{\mu]}{}^b e^{\rho a} - 
   \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\ 
\omega_{\mu}{}^{ab} 
&= e^{\nu b}\partial_{[\mu} e_{\nu]}{}^a + 
   e^{\nu a}\partial_{[\nu} e_{\mu]}{}^b -
   e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\lambda} e_{\rho]}{}^c
\\ 
\omega_{\mu}{}^{ab} 
&= 2 e^{\nu [b}\partial_{[\mu} e_{\nu]}{}^{a]} +
     e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\rho} e_{\lambda]}{}^c
\\ 
\omega_{\mu}{}^{ab} 
&= -2 e^{\nu [a}\partial_{[\mu} e_{\nu]}{}^{b]} 
   +e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\rho} e_{\lambda]}{}^c
\end{align*}
\end{document}
2
  • 1
    Thank you! i never knew about \tfrac and also the spacing between equations is a nice touch! :D thank you for your help :) – Lopey Tall Jun 11 '20 at 13:03
  • @LopeyTall - Glad you found my answer helpful. :-) – Mico Jun 11 '20 at 15:10
0

The derivation is hard to follow without any explanation; aligning the equals signs doesn't really help, in my opinion.

I propose left alignment throughout, with the longer equations split at the equals sign, slightly moved to the right.

\documentclass{article}
\usepackage[a4paper,margin=2.5cm]{geometry}
\usepackage{amsmath,mathtools}

\begin{document}

\begin{equation}
\begin{aligned}[t] 
& 0 = 0+0+0 \\[1ex]
& 0 = R_{\mu\nu}{}^a e_{\rho a} + R_{\rho\mu}{}^a e_{\nu a} -R_{\nu\rho}{}^a e_{\mu a}
\\[1ex]
& R_{\nu\rho}{}^a e_{\mu a} = R_{\mu\nu}{}^a e_{\rho a} + R_{\rho\mu}{}^a e_{\nu a}
\\[1ex]
& (
   \partial_{[\nu} e_{\rho]}{}^a -
   \omega_{[\nu}{}^{ab} e_{\rho]}{}_b
  ) e_{\mu a}
   = (
      \partial_{[\mu} e_{\nu]}{}^a - \omega_{[\mu}{}^{ab} e_{\nu]}{}_b
     ) e_{\rho a} +
     (
      \partial_{[\rho} e_{\mu]}{}^a - \omega_{[\rho}{}^{ab} e_{\mu]}{}_b
     ) e_{\nu a}
\\[1ex]
& \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} -
  \omega_{[\nu}{}^{ab} e_{\rho]}{}_b e_{\mu a}
  = \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} -
    \omega_{[\mu}{}^{ab} e_{\nu]}{}_b e_{\rho a} +
    \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} -
    \omega_{[\rho}{}^{ab} e_{\mu]}{}_b e_{\nu a}
\\[1ex]
& \omega_{[\mu}{}^{ab} e_{\nu]}{}{}_b e_{\rho a} +
  \omega_{[\rho}{}^{ab} e_{\mu]}{}_b e_{\nu a} -
  \omega_{[\nu}{}^{ab} e_{\rho]}{}_b e_{\mu a}
  = \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  +
    \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} -
    \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} \\[1ex]
& \tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} - 
  \tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a} +
  \tfrac{1}{2} \omega_{\rho}{}^{ab} e_{\mu}{}_b e_{\nu a} -
  \tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\rho}{}_b e_{\nu a} -
  \tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\rho}{}_b e_{\mu a} +
  \tfrac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} \\
& \qquad = \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  + 
    \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} -
    \partial_{[\nu} e_{\rho]}{}^a e_{\mu a}
\\[1ex]
&\bigl(
   \tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} -
   \tfrac{1}{2}\omega_{\mu}{}^{ba} e_{\rho}{}_a e_{\nu b}
 \bigr) +
 \bigl(
   \tfrac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} +
   \tfrac{1}{2} \omega_{\rho}{}^{ba} e_{\mu}{}_a e_{\nu b}
 \bigr) +
 \bigl(
   -\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a} -
   \tfrac{1}{2}\omega_{\nu}{}^{ba} e_{\rho}{}_a e_{\mu b}
 \bigr)\\
 & \qquad=   \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  +
   \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} -
   \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\[1ex]
&\bigl(
   \tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} +
   \tfrac{1}{2}\omega_{\mu}{}^{ab} e_{\rho}{}_a e_{\nu b}
 \bigr) +
 \bigl(
   \tfrac{1}{2}\omega_{\rho}{}^{ab} e_{\nu}{}_b e_{\mu a} -
   \tfrac{1}{2} \omega_{\rho}{}^{ab} e_{\mu}{}_a e_{\nu b}
 \bigr) +
 \bigl(
   -\tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\mu}{}{}_b e_{\rho a} +
   \tfrac{1}{2}\omega_{\nu}{}^{ab} e_{\rho}{}_a e_{\mu b}
 \bigr)\\
& \qquad= \partial_{[\mu} e_{\nu]}{}^a e_{\rho a} +
    \partial_{[\rho} e_{\mu]}{}^a e_{\nu a} -
    \partial_{[\nu} e_{\rho]}{}^a e_{\mu a} 
\\[1ex]
&\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a}  + 0 + 0 
  = \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}  +
    \partial_{[\rho} e_{\mu]}{}^c e_{\nu c} -
    \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} 
\\[1ex]
&\omega_{\mu}{}^{ab} e_{\nu}{}{}_b e_{\rho a} e^{\rho a} e^{\nu b}
  = \partial_{[\mu} e_{\nu]}{}^a e_{\rho a}e^{\rho a} e^{\nu b}  +
    \partial_{[\rho} e_{\mu]}{}^c e_{\nu c}e^{\rho a} e^{\nu b} -
    \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\[1ex]
&\omega_{\mu}{}^{ab} 
  = \partial_{[\mu} e_{\nu]}{}^a  e^{\nu b} +
    \partial_{[\rho} e_{\mu]}{}^c \delta_c^b e^{\rho a} -
    \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\[1ex]
&\omega_{\mu}{}^{ab}
  = \partial_{[\mu} e_{\nu]}{}^a  e^{\nu b}  +
    \partial_{[\rho} e_{\mu]}{}^b e^{\rho a} -
    \partial_{[\nu} e_{\rho]}{}^c e_{\mu c} e^{\rho a} e^{\nu b}
\\[1ex]
&\omega_{\mu}{}^{ab}
  = e^{\nu b}\partial_{[\mu} e_{\nu]}{}^a +
    e^{\nu a}\partial_{[\nu} e_{\mu]}{}^b -
    e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\lambda} e_{\rho]}{}^c
\\[1ex]
&\omega_{\mu}{}^{ab}
  = 2 e^{\nu [b}\partial_{[\mu} e_{\nu]}{}^{a]} +
    e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\rho} e_{\lambda]}{}^c
\\[1ex]
&\omega_{\mu}{}^{ab}
  = -2 e^{\nu [a}\partial_{[\mu} e_{\nu]}{}^{b]} +
    e^{\rho a} e^{\lambda b} e_{\mu c} \partial_{[\rho} e_{\lambda]}{}^c
\end{aligned}
\end{equation}

\end{document}

Some additional spacing between equations helps in distinguishing them.

However, I'd really prefer if there were comments at each main step.

enter image description here

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