Answer
$n=-9$ and $n=9$.
Work Step by Step
The given polynomial is
$\Rightarrow n^2-81=0$
Write the the polynomial as $a^2-b^2$.
$\Rightarrow n^2-9^2=0$
Use difference of two square pattern
$a^2-b^2=(a+b)(a-b)$.
We have $a=n$ and $b=9$.
$\Rightarrow (n+9)(n-9)=0$.
Use zero product property.
$\Rightarrow n+9=0$ or $n-9=0$.
Solve for $n$.
$\Rightarrow n=-9$ or $n=9$
Hence, the solutions are $n=-9$ and $n=9$.
