Answer
$n=3$.
Work Step by Step
The given polynomial is
$\Rightarrow n^2+9=6n$
Subtract $6n$ from each side.
$\Rightarrow n^2+9-6n=6n-6n$
Simplify.
$\Rightarrow n^2-6n+9=0$
Write the the polynomial as $a^2-2ab+b^2$.
$\Rightarrow n^2-2(n)(3)+3^2=0$.
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$.
We have $a=n$ and $b=3$.
$\Rightarrow (n-3)^2=0$.
Use zero product property.
$\Rightarrow n-3=0$.
Solve for $n$.
$\Rightarrow n=3$.
Hence, the solution is $n=3$.
