Answer
$q=-\frac{3}{4}$ and $q=-2$.
Work Step by Step
The given equation is
$\Rightarrow (4q+3)(q+2)=0$
Use zero-product property rule.
$\Rightarrow 4q+3=0$ or $q+2=0$
Solve for $q$.
$\Rightarrow q=-\frac{3}{4}$ or $q=-2$
Check:-
$q=-\frac{3}{4}$
$\Rightarrow (4(-\frac{3}{4})+3)(-\frac{3}{4}+2)=0$
$\Rightarrow (-3+3)(\frac{5}{4})=0$
$\Rightarrow 0(\frac{5}{4})=0$
$\Rightarrow 0=0$
True.
Check:-
$q=-2$
$\Rightarrow (4(-2)+3)(-2+2)=0$
$\Rightarrow (-8+3)(0)=0$
$\Rightarrow (-5)0=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $q=-\frac{3}{4}$ and $q=-2$.
