Answer
$q=0$ or $q=9$.
Work Step by Step
The given equation is
$\Rightarrow 18q-2q^2=0$
Factor out $2q$.
$\Rightarrow 2q(9-q)=0$
Use zero-product property rule.
$\Rightarrow 2q=0$ or $9-q=0$
Solve for $q$.
$\Rightarrow q=0$ or $q=9$
Check:-
$q=0$
$\Rightarrow 18(0)-2(0)^2=0$
$\Rightarrow 0+0=0$
$\Rightarrow 0=0$
True.
Check:-
$q=9$
$\Rightarrow 18(9)-2(9)^2=0$
$\Rightarrow 162-2(81)=0$
$\Rightarrow 162-162=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $q=0$ or $q=9$.
