\begin{equation*}
    \begin{split}
        \,& T(z_1) = T(z_2) \Leftrightarrow \frac{az_1 + b}{cz_1 + d} = \frac{az_2 + b}{cz_2 + d} \\
        & \Leftrightarrow (az_1 + b)(cz_2 + d) = (cz_1 + d)(az_2 + b)
    \end{split}
\end{equation*}