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This question already has an answer here:

Any help is most appreciated. Thanks!

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtool}
\begin{document}
\begin{align}
\begin{split}
& v \cdot \left\{ Ax + b \\
& Cx - d \right\}
\end{split}
\end{align}
\end{document}

marked as duplicate by egreg, Manuel, Werner, Sean Allred, Jesse Aug 30 '14 at 18:21

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The breqn package for breaking equations can be used for this purpose. Albeit I think this is a trivial case to apply such a package in. The code using brepn is as follows:

\documentclass{article}
\usepackage{breqn}
\begin{document}

\begin{dmath}
 v \cdot \left\{Ax+ b \linebreak
 Cx - d \right\}
\end{dmath}

\end{document}

The output in this case:

enter image description here

Other wise, without using breqn one can insert \left . and \right . to balance the curly brackets since no \\ is allowable inside curly brackets.

The output of the first method is not satisfying, so I suggest in this case it is better to use the aligned environment taking into consideration balancing curly braces as mentioned above. Here is the code:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation}
\begin{aligned}
 v \cdot \left\{ \right . Ax &+ b \\
 Cx &- d \left . \right\}
\end{aligned}
\end{equation}

\end{document}

And the output is much better:

enter image description here

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