Answer
$(2m-9)(6m+11n)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
12m^2-54m+22mn-99n
,$ group the terms such that the factored form of the groupings will result to a factor that is common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(12m^2-54m)+(22mn-99n)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
6m(2m-9)+11n(2m-9)
.\end{array}
Factoring the $GCF=
(2m-9)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2m-9)(6m+11n)
.\end{array}
