Answer
$a=3$ and $a=-5$.
Work Step by Step
The given equation is
$\Rightarrow (2a-6)(3a+15)=0$
Use zero-product property rule.
$\Rightarrow 2a-6=0$ or $3a+15=0$
Solve for $a$.
$\Rightarrow a=3$ or $a=-5$
Check:-
$a=3$
$\Rightarrow (2(3)-6)(3(3)+15)=0$
$\Rightarrow (6-6)(9+15)=0$
$\Rightarrow 0(24)=0$
$\Rightarrow 0=0$
True.
Check:-
$a=-5$
$\Rightarrow (2(-5)-6)(3(-5)+15)=0$
$\Rightarrow (-10-6)(-15+15)=0$
$\Rightarrow (-16)0=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $a=3$ and $a=-5$.
