Answer
$m=0$ and $m=-2$.
Work Step by Step
The given equation is
$\Rightarrow 6m^2+12m=0$
Factor out $6m$.
$\Rightarrow 6m(m+2)=0$
Use zero-product property rule.
$\Rightarrow 6m=0$ or $m+2=0$
Solve for $m$.
$\Rightarrow m=0$ or $m=-2$
Check:-
$m=0$
$\Rightarrow 6(0)^2+12(0)=0$
$\Rightarrow 0+0=0$
$\Rightarrow 0=0$
True.
Check:-
$m=-2$
$\Rightarrow 6(-2)^2+12(-2)=0$
$\Rightarrow 6(4)-24=0$
$\Rightarrow 24-24=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $m=0$ and $m=-2$.
