Answer
$z=-9$.
Work Step by Step
The given equation is
$\Rightarrow z+3=-6$
Subtract $3$ from each side.
$\Rightarrow z+3-3=-6-3$
Simplify.
$\Rightarrow z=-9$
Check:-
$\Rightarrow -9+3=-6$
$\Rightarrow -6=-6$
True.
Hence, the solution is $z=-9$.