Answer
$(3m+1)(2m-5)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
6m^2-13m-5
,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
In the trinomial expression above the value of $ac$ is $
6(-5)=-30
$ and the value of $b$ is $
-13
.$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\{
2,-15
\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
6m^2+2m-15m-5
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(6m^2+2m)-(15m+5)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2m(3m+1)-5(3m+1)
.\end{array}
Factoring the $GCF=
(3m+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(3m+1)(2m-5)
.\end{array}
