Answer
$x=\left\{ -11,5 \right\}$
Work Step by Step
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
equation
}$
\begin{array}{l}\require{cancel}
x^2+6x-55
\end{array} has $c=
-55
$ and $b=
6
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
11,-5
\right\}.$ Using these two numbers, the $\text{
equation
}$ above is equivalent to
\begin{array}{l}\require{cancel}
(x+11)(x-5)=0
.\end{array}
Equating each factor to zero (Zero Product Property), and then isolating the variable, the solutions are $
x=\left\{ -11,5 \right\}
.$