\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{align*}
           &&                        0 &= \dfrac{1}{4}(2(-1) + 1) + C \mathrm{e}^{2(-1)} \\
  \implies &&                        0 &= \dfrac{-1}{4} + C \mathrm{e}^{-2}              \\
  \implies && \dfrac{1}{4}\mathrm{e}^2 &= C                                              \\
  \implies &&                        C &= \dfrac{1}{4}\mathrm{e}^2
\end{align*}

\begin{alignat*}{2}
           &&                        0 &= \dfrac{1}{4}(2(-1) + 1) + C \mathrm{e}^{2(-1)} \\
  \implies &&                        0 &= \dfrac{-1}{4} + C \mathrm{e}^{-2}              \\
  \implies && \dfrac{1}{4}\mathrm{e}^2 &= C                                              \\
  \implies &&                        C &= \dfrac{1}{4}\mathrm{e}^2
\end{alignat*}

\end{document}