Answer
$z=4$ and $z=6$.
Work Step by Step
The given equation is
$\Rightarrow (z-4)(z-6)=0$
Use zero-product property rule.
$\Rightarrow z-4=0$ or $z-6=0$
Solve for $z$.
$\Rightarrow z=4$ or $z=6$
Check:-
$z=4$
$\Rightarrow (4-4)(4-6)=0$
$\Rightarrow (0)(-2)=0$
$\Rightarrow 0=0$
True.
Check:-
$z=6$
$\Rightarrow (6-4)(6-6)=0$
$\Rightarrow 2(0)=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $z=4$ and $z=6$.