Answer
$z=-3$ or $z=7$.
Work Step by Step
The given equation is
$\Rightarrow (z+3)(z-7)=0$
Use zero-product property rule.
$\Rightarrow z+3=0$ or $z-7=0$
Solve for $z$.
$\Rightarrow z=-3$ or $z=7$
Hence, the solutions are $z=-3$ or $z=7$.