Answer
$y=6$.
Work Step by Step
The given polynomial is
$\Rightarrow y^2=12y-36$
Add $-12y+36$ to each side.
$\Rightarrow y^2-12y+36=12y-36-12y+36$
Simplify.
$\Rightarrow y^2-12y+36=0$
Write the the polynomial as $a^2-2ab+b^2$.
$\Rightarrow y^2-2(y)(6)+6^2=0$.
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$.
We have $a=y$ and $b=6$.
$\Rightarrow (y-6)^2=0$.
Use zero product property.
$\Rightarrow y-6=0$.
Solve for $y$.
$\Rightarrow y=6$.
Hence, the solution is $y=6$.
