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