Answer
$x=-\dfrac{5}{6}$
Work Step by Step
The two numbers whose product is $ac=
36(25)=900
$ and whose sum is $b=
60
$ are $\{
30,30
\}$. Using these two numbers to decompose the middle term of the given equation, $
36x^2+60x+25=0
,$ results to
\begin{array}{l}\require{cancel}
36x^2+30x+30x+25=0
\\\\
(36x^2+30x)+(30x+25)=0
\\\\
6x(6x+6)+5(6x+5)=0
\\\\
(6x+6)(6x+5)=0
.\end{array}
Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
6x+5=0
\\\\
6x=-5
\\\\
x=-\dfrac{5}{6}
,\\\\\text{OR}\\\\
6x+5=0
\\\\
6x=-5
\\\\
x=-\dfrac{5}{6}
.\end{array}
Hence, the solution is $
x=-\dfrac{5}{6}
.$
