Answer
$t=0$ and $t=5$.
Work Step by Step
The given equation is
$\Rightarrow 12t(t-5)=0$
Use zero-product property rule.
$\Rightarrow 12t=0$ or $t-5=0$
Solve for $t$.
$\Rightarrow t=0$ or $t=5$
Check:-
$t=0$
$\Rightarrow 12(0)(0-5)=0$
$\Rightarrow 0(-5)=0$
$\Rightarrow 0=0$
True.
Check:-
$t=5$
$\Rightarrow 12(5)(5-5)=0$
$\Rightarrow 60(0)=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $t=0$ and $t=5$.
