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}
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:

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:

\\between\leftand\rightdelimiters. See, for example, http://tex.stackexchange.com/questions/5612/left-right-across-multi-line-equation – Adam Liter Aug 30 '14 at 17:26