Answer
$s=-\frac{5}{3}$ and $s=-\frac{8}{5}$.
Work Step by Step
The given equation is
$\Rightarrow (3s+5)(5s+8)=0$
Use zero-product property rule.
$\Rightarrow 3s+5=0$ or $5s+8=0$
Solve for $s$.
$\Rightarrow s=-\frac{5}{3}$ or $s=-\frac{8}{5}$
Check:-
$s=-\frac{5}{3}$
$\Rightarrow (3(-\frac{5}{3})+5)(5(-\frac{5}{3})+8)=0$
$\Rightarrow (-5+5)(-\frac{25}{3}+8)=0$
$\Rightarrow 0(-\frac{1}{3})=0$
$\Rightarrow 0=0$
True.
Check:-
$s=-\frac{8}{5}$
$\Rightarrow (3(-\frac{8}{5})+5)(5(-\frac{8}{5})+8)=0$
$\Rightarrow (-\frac{24}{5}+5)(-8+8)=0$
$\Rightarrow (\frac{1}{5})(0)=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $s=-\frac{5}{3}$ and $s=-\frac{8}{5}$.
