Equations that will not fit

Sooner or later a derivation produces an equation wider than the text block, and LaTeX will let it run into the margin rather than guess where to break it. Two amsmath environments let you place the break yourself: multline for a single long expression, and split for a break that should stay aligned.

multline

\begin{multline}
 a + b + c + d + e + f \\
 + g + h + i + j
\end{multline}

multline suits one long formula with no natural alignment point. You choose the break with \\, and the environment handles the layout: the first line is set flush left, the last flush right, and any middle lines are centered. The whole expression gets one equation number, placed on the last line. Convention is to break before a binary operator, so the + opens the continuation line and the reader sees at a glance that the expression carries on.

split

\begin{equation}
\begin{split}
 a &= b + c \\
 &\quad + d + e
\end{split}
\end{equation}

split also produces a single number, but aligns its lines the way align does, with & marking the alignment point. It is not a standalone environment; it lives inside equation or another display environment, which supplies the number. Here the & sits before the equals sign on the first line, and the continuation starts with &\quad, an empty alignment point followed by a quad of space, so the second line indents just past the equals sign. That indent tells the reader this is still the right-hand side, not a new equation.

Choosing between them

Use multline when the equation is one long sum with no structure worth aligning. Use split when there is an equals sign the continuation should hang under. If you have several genuinely separate equations, neither is right; that is a job for align, covered in multi-line equations that line up.

Before reaching for either, consider rewriting the math. Naming a subexpression in the preceding sentence, factoring, or splitting the statement into two equations often brings the width under control and improves readability at the same time. Prefer that over shrinking the type; a display squeezed to fit almost always reads worse than a clean break.

One error to know: split used on its own, without an enclosing equation, stops with a “Package amsmath Error”. Wrap it first, then compile. Both environments are quick to experiment with in the live playground.