Answer
$r=0$ or $r=-7$.
Work Step by Step
The given equation is
$\Rightarrow -28r=4r^2$
Add $28r$ to each side.
$\Rightarrow -28r+28r=4r^2+28r$
Simplify.
$\Rightarrow 0=4r^2+28r$
Factor out $4r$.
$\Rightarrow 0=4r(r+7)$
Use zero-product property rule.
$\Rightarrow 4r=0$ or $r+7=0$
Solve for $r$.
$\Rightarrow r=0$ or $r=-7$
Check:-
$r=0$
$\Rightarrow -28(0)=4(0)^2$
$\Rightarrow -28(0)=4(0)$
$\Rightarrow 0=0$
True.
Check:-
$r=-7$
$\Rightarrow -28(-7)=4(-7)^2$
$\Rightarrow -28(-7)=4(49)$
$\Rightarrow 196=196$
True.
Hence, the solutions are $r=0$ or $r=-7$.
