$\begin{array} { l }t+\frac{ 72 }{ t }=-17,& t≠0\end{array}$
$t+\frac{ 72 }{ t }+17=0$
$\frac{ {t}^{2}+72+17t }{ t }=0$
${t}^{2}+72+17t=0$
${t}^{2}+17t+72=0$
${t}^{2}+9t+8t+72=0$
$t \times \left( t+9 \right)+8t+72=0$
$t \times \left( t+9 \right)+8\left( t+9 \right)=0$
$\left( t+9 \right) \times \left( t+8 \right)=0$
$\begin{array} { l }t+9=0,\\t+8=0\end{array}$
$\begin{array} { l }t=-9,\\t+8=0\end{array}$
$\begin{array} { l }\begin{array} { l }t=-9,\\t=-8\end{array},& t≠0\end{array}$
$\begin{array} { l }t=-9,\\t=-8\end{array}$
$\begin{array} { l }t_1=-9,& t_2=-8\end{array}$