equation crossed the margin (A very very long equation)

Question

Here is my equation:

\documentclass{article}
\usepackage{amsmath} % for 'align*' environment

\begin{document}

    \begin{equation} \label{eq:Vo}
        V_o = \frac{ L_3 R_3 R_L + L_3 R_2 R_L s + R_2 R_3 R_L}{X}
    \end{equation}
        where
        \begin{align*}
        X&=\bigl( C_2 C_1 L_2 L_3 R_1 R_3 R_L + C_2 C_1 L_2 L_3 R_1 R_2 R_L + C_2 C_1 L_1 L_3 R_1 R_3 R_L + C_2 C_1 L_1 L_3 R_1 R_2 R_L + C_2 C_1 L_1 L_2 R_1 R_3 R_L + C_2 C_1 L_1 L_2 R_1 R_2 R_L\bigr) s^4 \\
        &\quad+ \bigl(C_2 C_1 L_2 R_1 R_2 R_3 R_L + C_2 C_1 L_1 R_1 R_2 R_3 R_L + C_1 L_2 L_3 R_1 R_3 + C_1 L_2 L_3 R_1 R_2 + C_1 L_1 L_3 R_1 R_3 + C_1 L_1 L_3 R_1 R_2 + C_1 L_1 L_2 R_1 R_3 + C_1 L_1 L_2 R_1 R_2 + C_2 L_2 L_3 R_3 R_L + C_2 L_2 L_3 R_2 R_L + C_2 L_1 L_3 R_3 R_L + C_2 L_1 L_3 R_2 R_L + C_2 L_1 L_2 R_3 R_L + C_2 L_1 L_2 R_2 R_L\bigr) s^3 \\
        &\quad+ \bigl(C_1 L_3 R_1 R_3 R_L + C_1 L_3 R_1 R_2 R_L + C_1 L_2 R_1 R_2 R_3 + C_1 L_1 R_1 R_3 R_L + C_1 L_1 R_1 R_2 R_L + C_1 L_1 R_1 R_2 R_3 + C_2 L_3 R_1 R_3 R_L + C_2 L_3 R_1 R_2 R_L + C_2 L_2 R_2 R_3 R_L + C_2 L_2 R_1 R_3 R_L + C_2 L_2 R_1 R_2 R_L + C_2 L_1 R_2 R_3 R_L + L_2 L_3 R_3 + L_2 L_3 R_2 + L_1 L_3 R_3 + L_1 L_3 R_2 + L_1 L_2 R_3 + L_1 L_2 R_2\bigr) s^2 \\
        &\quad+ \bigl(C_1 R_1 R_2 R_3 R_L + C_2 R_1 R_2 R_3 R_L + L_3 R_3 R_L + L_3 R_2 R_L + L_3 R_1 R_3 + L_3 R_1 R_2 + L_2 R_2 R_3 + L_2 R_1 R_3 + L_2 R_1 R_2 + L_1 R_3 R_L + L_1 R_2 R_L + L_1 R_2 R_3\bigr) s + \bigl(R_2 R_3 R_L + R_1 R_3 R_L + R_1 R_2 R_L + R_1 R_2 R_3\bigr)
        \end{align*}

\end{document}

I tried few methods that were the answers to some other questions on this same forum, but not worked, the equation runs out of margin.

Why cant there be a method which allows the ex: /quad to continue on to the next line when the margin end is encountered ?

Does someone know a trick which does stop at margin and continue where it had left from a new line until it ends and a new /quad begins.

Thanks in advance.

Answer 1

You could do this, but is it not possible to change the notation? No one is going to read this. With this layout if one of the R_2 should be a C_1 it would be very hard to ever spot the error...

\documentclass{amsart}
\begin{document}

\begin{equation} \label{eq:serial_Vo}
V_o = \frac{ L_3 R_3 R_L + L_3 R_2 R_L s + R_2 R_3 R_L}{X}
\end{equation}
where
\begin{flushleft}
\hangindent=3em
$
X=\bigl( C_2 C_1 L_2 L_3 R_1 R_3 R_L + C_2 C_1 L_2 L_3 R_1 R_2 R_L + C_2 C_1 L_1 L_3 R_1 R_3 R_L + C_2 C_1 L_1 L_3 R_1 R_2 R_L + C_2 C_1 L_1 L_2 R_1 R_3 R_L + C_2 C_1 L_1 L_2 R_1 R_2 R_L\bigr) s^4 
+ \bigl(C_2 C_1 L_2 R_1 R_2 R_3 R_L + C_2 C_1 L_1 R_1 R_2 R_3 R_L + C_1 L_2 L_3 R_1 R_3 + C_1 L_2 L_3 R_1 R_2 + C_1 L_1 L_3 R_1 R_3 + C_1 L_1 L_3 R_1 R_2 + C_1 L_1 L_2 R_1 R_3 + C_1 L_1 L_2 R_1 R_2 + C_2 L_2 L_3 R_3 R_L + C_2 L_2 L_3 R_2 R_L + C_2 L_1 L_3 R_3 R_L + C_2 L_1 L_3 R_2 R_L + C_2 L_1 L_2 R_3 R_L + C_2 L_1 L_2 R_2 R_L\bigr) s^3 
+ \bigl(C_1 L_3 R_1 R_3 R_L + C_1 L_3 R_1 R_2 R_L + C_1 L_2 R_1 R_2 R_3 + C_1 L_1 R_1 R_3 R_L + C_1 L_1 R_1 R_2 R_L + C_1 L_1 R_1 R_2 R_3 + C_2 L_3 R_1 R_3 R_L + C_2 L_3 R_1 R_2 R_L + C_2 L_2 R_2 R_3 R_L + C_2 L_2 R_1 R_3 R_L + C_2 L_2 R_1 R_2 R_L + C_2 L_1 R_2 R_3 R_L + L_2 L_3 R_3 + L_2 L_3 R_2 + L_1 L_3 R_3 + L_1 L_3 R_2 + L_1 L_2 R_3 + L_1 L_2 R_2\bigr) s^2 
+ \bigl(C_1 R_1 R_2 R_3 R_L + C_2 R_1 R_2 R_3 R_L + L_3 R_3 R_L + L_3 R_2 R_L + L_3 R_1 R_3 + L_3 R_1 R_2 + L_2 R_2 R_3 + L_2 R_1 R_3 + L_2 R_1 R_2 + L_1 R_3 R_L + L_1 R_2 R_L + L_1 R_2 R_3\bigr) s + 
\bigl(R_2 R_3 R_L + R_1 R_3 R_L + R_1 R_2 R_L + R_1 R_2 R_3\bigr)
$
\end{flushleft}

\end{document}