Answer
$g=\frac{3}{2}$ and $g=7$.
Work Step by Step
The given equation is
$\Rightarrow (3-2g)(7-g)=0$
Use zero-product property rule.
$\Rightarrow 3-2g=0$ or $7-g=0$
Solve for $g$.
$\Rightarrow 3=2g$ or $7=g$
$\Rightarrow \frac{3}{2}=g$ or $7=g$
Check:-
$g=\frac{3}{2}$
$\Rightarrow (3-2(\frac{3}{2}))(7-\frac{3}{2})=0$
$\Rightarrow (3-3)(\frac{11}{2})=0$
$\Rightarrow (0)(\frac{11}{2})=0$
$\Rightarrow 0=0$
True.
Check:-
$g=7$
$\Rightarrow (3-2(7))(7-7)=0$
$\Rightarrow (3-14)(0)=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $g=\frac{3}{2}$ and $g=7$.
