\documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amscd,concmath,amsfonts}
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\begin{document}
\begin{equation*}
  \aligned 
    -g \sin z_{3,e} &= 0 \\
    g (\cos z_{3,e} - 1)  &= 0
  \endaligned  
  \qquad\implies\qquad
  z_{3,e} = \theta_e = 0.
\end{equation*}
\end{document}