Answer
{$-\frac{3}{5}$}
Work Step by Step
$25x^{2}+30x+9=0$
$25x^{2}+15x+15x+9=0$
$5x(5x+3)+3(5x+3)=0$
$(5x+3)(5x+3)=0$
$(5x+3)=0$ or $(5x+3)=0$
$x=-\frac{3}{5}$ or $x=-\frac{3}{5}$
Check:
Substituting $x=-\frac{3}{5}$ in the equation,
$25(-\frac{3}{5})^{2}+30(-\frac{3}{5})+9=0$
$\frac{25\times9}{25}-\frac{30\times3}{5}+9=0$
$9-18+9=0$
$0=0$
The value checks and the solution set is {$-\frac{3}{5}$}
