#### Answer

$x=-\dfrac{3}{5}$

#### Work Step by Step

The two numbers whose product is $ac=
25(9)=225
$ and whose sum is $b=
30
$ are $\{
15,15
\}$. Using these two numbers to decompose the middle term of the given equation, $
25x^2+30x+9=0
,$ results to
\begin{array}{l}\require{cancel}
25x^2+15x+15x+9=0
\\\\
(25x^2+15x)+(15x+9)=0
\\\\
5x(5x+3)+3(5x+3)=0
\\\\
(5x+3)(5x+3)=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}
5x+3=0
\\\\
5x=-3
\\\\
x=-\dfrac{3}{5}
,\\\\\text{OR}\\\\
5x+3=0
\\\\
5x=-3
\\\\
x=-\dfrac{3}{5}
.\end{array}
Hence, the solution is $
x=-\dfrac{3}{5}
.$