#### Answer

$(6m-5)^2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $ax^2+bx+c,$ find two numbers whose product is $ac$ and whose sum is $b$. Use these $2$ numbers to decompose the middle term of the quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
In the given expression, $
36m^2-60m+25
,$ the value of $ac$ is $
36(25)=900
$ and the value of $b$ is $
-60
.$ The $2$ numbers that have a product $ac$ and a sum of $b$ are $\{
-30,-30
\}.$ Using these $2$ numbers to decompose the middle term of the given expression results to
\begin{array}{l}\require{cancel}
36m^2-30m-30m+25
.\end{array}
Grouping the first and third terms and the second and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(36m^2-30m)-(30m-25)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
6m(6m-5)-5(6m-5)
.\end{array}
Factoring the $GCF=
(6m-5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(6m-5)(6m-5)
\\\\=
(6m-5)^2
.\end{array}