\documentclass[12pt]{article}
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\begin{document}
\begin{equation*}
  \aligned 
    P[k+1] &= A P[k] A^T + F R_v F^T - A P[k] C^T L^T - L C P[k] A^T +
      L R_\epsilon L^T \\ 
    &= A P[k] A^T + F R_v F^T +
      \bigl(L \!-\! A P[k] C^T R_\epsilon^{-1} \bigr) R_\epsilon 
      \bigl(L \!-\! A P[k] C^T R_\epsilon^{-1} \bigr)^T \\
    &\qquad - A P[k] C^T R_\epsilon^{-1} C P^T[k] A^T.
  \endaligned
\end{equation*}
\end{document}