Answer
$z=\{ -7,3 \}$
Work Step by Step
By the Zero-Product Property, $ab=0$ implies $a=0 \text{ OR } b=0$. Hence, the solution to the given equation, $
(z-3)(z+7)=0
$, is
\begin{array}{}
z-3=0
\\
z=0+3
\\
z=3
,\\\\\text{OR}\\\\
z+7=0
\\
z=0-7
\\
z=-7
.\end{array}
Hence, $
z=\{ -7,3 \}
$.
