Answer
$\color{blue}{\left\{-9, -3\right\}}$
Work Step by Step
RECALL:
A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$.
The trinomial's factored form will be:
$x^2+bx+c=(x+d)(x+e)$
The trinomial in the given equation has $b=12$ and $c=27$.
Note that $27=9(3)$ and $12= 9+3$.
This means that $d=9$ and $e=3$
Thus, the factored form of the trinomial is: $(h+9)(h+3)$
The given equation maybe written as:
$(h+9)(h+3)=0$
Use the Zero-Factor Property by equating each factor to zero.
Then, solve each equation to obtain:
\begin{array}{ccc}
&h+9 = 0 &\text{ or } &h+3=0
\\&h=-9 &\text{ or } &h=-3
\end{array}
Thus, the solution set is $\color{blue}{\left\{-9, -3\right\}}$.
