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My MWE:

\documentclass{report}

\usepackage{amsmath}

\begin{document}

\begin{align}
y &= a \\
=& -2c_1\bar{z}_1^2 + 2\bar{z}_1\bar{z}_2 + 2\bar{z}_2 \left ( -\bar{z}_1 -c_2z_2 - \frac{3\epsilon}{2}\bar{z}_2 -\sigma_{2,1}\cos(x_1)\Delta x_1 \notag \right. \\
\left. &- \sigma_{2,2}\Delta x_2 -\sigma_{2,3} \Delta u +c_2 \chi_2 \vphantom{\frac{1}{1}} \right ) - 2\gamma \sigma_{2,1}^2\cos^2(x_1) \Delta x_1^2 - \gamma \sigma_{2,2}^2 \Delta x_2^2   - 2\gamma \sigma_{2,3}^2 \Delta u^2
\end{align}

\end{document}

The error I get:

Extra }, or forgotten \right.

The expected result:

enter image description here

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3  
The alignment character & cannot be inside the pair \left, \right –  Gonzalo Medina Jul 22 at 18:21
2  
\left and \right can't be separated by & or \\ . you have \left. all alone at the beginning of the second line, before the &. (and this question has been asked many times before. here's just one instance: Using \left( & \right) around amsmath's align delimiter (“&”)) –  barbara beeton Jul 22 at 18:24

2 Answers 2

up vote 4 down vote accepted

If you only want your code to be compilable, \left. should be moved to the next column. But many additional changes are needed for a proper appearance. Some suggestions are in the second example.

\documentclass{report}

\usepackage{amsmath}

\begin{document}

\begin{align}
y &= a \\
=& -2c_1\bar{z}_1^2 + 2\bar{z}_1\bar{z}_2 + 2\bar{z}_2 \left ( 
-\bar{z}_1 -c_2z_2 - \frac{3\epsilon}{2}\bar{z}_2 -\sigma_{2,1}\cos(x_1)\Delta x_1 \notag 
\right. \\
 &\left.- \sigma_{2,2}\Delta x_2 -\sigma_{2,3} \Delta u +c_2 \chi_2 \vphantom{\frac{1}{1}} \right ) - 2\gamma \sigma_{2,1}^2\cos^2(x_1) \Delta x_1^2 - \gamma \sigma_{2,2}^2 \Delta x_2^2   - 2\gamma \sigma_{2,3}^2 \Delta u^2
\end{align}

\begin{align}
y &= a \notag\\
& = -2c_1\bar{z}_1^2 + 2\bar{z}_1\bar{z}_2 \notag\\
& {}+ 2\bar{z}_2 \left ( 
-\bar{z}_1 -c_2z_2 - \frac{3\epsilon}{2}\bar{z}_2 -\sigma_{2,1}\cos(x_1)\Delta x_1 - \sigma_{2,2}\Delta x_2 -\sigma_{2,3} \Delta u +c_2 \chi_2 \vphantom{\frac{1}{1}} \right )\notag\\
& - 2\gamma \sigma_{2,1}^2\cos^2(x_1) \Delta x_1^2 - \gamma \sigma_{2,2}^2 \Delta x_2^2   - 2\gamma \sigma_{2,3}^2 \Delta u^2
\end{align}

\end{document}

enter image description here

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As others have already pointed out, the error message you get arises because the directives \left. and \right) are separated by an & alignment character. While moving the \left. instruction to after the & character will get rid of the immediate error, the layout of the equation still isn't great. In particular, the automatically sized parentheses produced by \left and \right are much too large and end up visually dominating the entire group of equations. I think you're better off using \Bigl( and \Bigr, i.e., not using auto-sized parentheses.

Your equation may also benefit from being broken up across three instead of just two lines.

enter image description here

\documentclass{report}
\usepackage{amsmath}
\begin{document}
\begin{align}
y &= a \notag\\
&= -2c_1\bar{z}_1^2 + 2\bar{z}_1\bar{z}_2 + 2\bar{z}_2 \Bigl( -\bar{z}_1 -c_2z_2 - \frac{3\epsilon}{2}\bar{z}_2 -\sigma_{2,1}\cos(x_1)\Delta x_1 \notag \\
&\qquad- \sigma_{2,2}\Delta x_2 -\sigma_{2,3} \Delta u +c_2 \chi_2 \vphantom{\frac{1}{1}} \Bigr) - 2\gamma \sigma_{2,1}^2\cos^2(x_1) \Delta x_1^2 \notag\\
&\qquad- \gamma \sigma_{2,2}^2 \Delta x_2^2   - 2\gamma \sigma_{2,3}^2 \Delta u^2
\end{align}
\end{document}
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