Looking for a better layout or style in writing solutions of equations

Before I proceed to write a lot of solutions, I want to adopt a style that I will use consistently in my document. So far I write a solution of an equation as follows. Could you review this ? Any comment, suggestions, improvements to make mine better, more readable, etc are always welcome.

\documentclass[border=12pt,preview]{standalone}
\usepackage{amsmath}
\begin{document}
Solve $-5(1 - 7 x) (3 x + 10) (2 x + 1)=0$ with  factorization.
\begin{gather*}
-5(1 - 7 x) (3 x + 10) (2 x + 1)=0\\
\begin{aligned}[t]
x &= \frac{-1}{-7}\\
&= \frac{1}{7}
\begin{aligned}[t]
x &= \frac{-10}{3}\\
&= -\frac{10}{3}
\end{aligned}
\begin{aligned}[t]
x &= \frac{-1}{2}\\
&= -\frac{1}{2}
\end{aligned}
\end{gather*}
Thus the solution is $x\in \{-\frac{10}{3},-\frac{1}{2},\frac{1}{7}\}$.
\end{document}

• I like your layout... except the = and ors are not vertically aligned. So, why not try \begin{align*} and \end{align*} ...instead of \begin{gather*} and \end{gather*} ? Sep 21, 2020 at 8:13

Does this look to be a better way to align your equations...

\documentclass[border=12pt,preview]{standalone}
\usepackage{amsmath}

\newcommand{\nxt}{&          &&}  %%  next column
\newcommand{\nxr}{&\text{or} &&}  %%  next column with "or"

\begin{document}

Solve $-5(1 - 7 x) (3 x + 10) (2 x + 1)=0$ with  factorization.
%
\begin{align*}
-5(1 - 7 x) (3 x + 10) (2 x + 1) = 0
\end{align*}
%
\begin{align*}
1-7x &=  0            \nxr    3x+10 &=   0           \nxr      2x+1 &=  0 \\
-7x &= -1            \nxr    3x    &= -10           \nxr      2x   &= -1 \\
x &= \frac{-1}{-7} \nxr     x    &= \frac{-10}{3} \nxr       x   &= \frac{-1}{2} \\
&= \frac{1}{7}   \nxt          &= -\frac{10}{3} \nxt           &= -\frac{1}{2}
\end{align*}
%
Thus the solution is $x\in \{-\frac{10}{3},-\frac{1}{2},\frac{1}{7}\}$.

\end{document}

• OK. Thank you. Looks more readable! Sep 21, 2020 at 10:09
• Good to know you liked it. Sep 21, 2020 at 12:05