Answer
$c=0$ or $c=-\frac{5}{2}$.
Work Step by Step
The given equation is
$\Rightarrow 25c+10c^2=0$
Factor out $5c$.
$\Rightarrow 5c(5+2c)=0$
Use zero-product property rule.
$\Rightarrow 5c=0$ or $5+2c=0$
Solve for $c$.
$\Rightarrow c=0$ or $c=-\frac{5}{2}$
Check:-
$c=0$
$\Rightarrow 25(0)+10(0)^2=0$
$\Rightarrow 0+0=0$
$\Rightarrow 0=0$
True.
Check:-
$c=-\frac{5}{2}$
$\Rightarrow 25(-\frac{5}{2})+10(-\frac{5}{2})^2=0$
$\Rightarrow -\frac{125}{2}+10(\frac{25}{4})=0$
$\Rightarrow -\frac{125}{2}+\frac{125}{2}=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $c=0$ or $c=-\frac{5}{2}$.
