Answer
$n=0$ or $n=3$.
Work Step by Step
The given equation is
$\Rightarrow 3n^2=9n$
Subtract $9n$ from each side.
$\Rightarrow 3n^2-9n=9n-9n$
Simplify.
$\Rightarrow 3n^2-9n=0$
Factor out $3n$.
$\Rightarrow 3n(n-3)=0$
Use zero-product property rule.
$\Rightarrow 3n=0$ or $n-3=0$
Solve for $n$.
$\Rightarrow n=0$ or $n=3$
Check:-
$n=0$
$\Rightarrow 3(0)^2=9(0)$
$\Rightarrow 3(0)=9(0)$
$\Rightarrow 0=0$
True.
Check:-
$n=3$
$\Rightarrow 3(3)^2=9(3)$
$\Rightarrow 3(9)=9(3)$
$\Rightarrow 27=27$
True.
Hence, the solutions are $n=0$ or $n=3$.
