Answer
$(x+3)(5x-2)$
Work Step by Step
Factor the given quadratic using the $ac$-method by performing the following steps:
(1) Find the value of $ac$. The given quadratic trinomial has $a=5, b=13, $ and $c=-6$.
Thus, $ac=5(-6)=-30$.
(2) Look for factors $d$ and $e$ of $-30$ whose sum is equal to $13$.
Note that: $-30=(15)(-2)$ and $15+(-2) = 13$.
Thus, $d=15$ and $e=-2$.
(3) Rewrite the quadratic trinomial as $ax^2+dx+ex+c$:
$$5x^2+13x-6=5x^2+15x-2x-6$$
(4) Factor $5x^2+15x-2x-6$ by grouping:
\begin{align*}
5x^2+15x-2x-6&=(5x^2+15x)+(-2x-6)\\
&=5x(x+3)+(-2)(x+3)\\
&=(x+3)(5x-2)
\end{align*}
