(Z-7/3)(-z-5/12)=(2z-27/15)

$$\\(Z-\frac{7}{3})(-z-\frac{5}{12})=(2z-\frac{27}{15})\\\\
$I'm going to multiply both sides by 180$\\\\
3(Z-\frac{7}{3})*60(-z-\frac{5}{12})=180(2z-\frac{27}{15})\\\\
(3z-7)(-60z-25)=360z-324\\\\
(3z-7)(60z+25)=324-360z\\\\
180z^2+75z-420z-175=324-360z\\\\
180z^2-345z+360z-175-324=0\\\\
180z^2+15z-499=0\\\\$$

 

Now finish it with the quadratic formula.

 

$${\mathtt{180}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{z}}{\mathtt{\,-\,}}{\mathtt{499}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{z}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{39\,945}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}\right)}{{\mathtt{120}}}}\\
{\mathtt{z}} = {\frac{\left({\sqrt{{\mathtt{39\,945}}}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}{{\mathtt{120}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{z}} = -{\mathtt{1.707\: \!187\: \!105\: \!848\: \!766\: \!1}}\\
{\mathtt{z}} = {\mathtt{1.623\: \!853\: \!772\: \!515\: \!432\: \!8}}\\
\end{array} \right\}$$

.