Answer
$\{0,5\}$.
Work Step by Step
The given equation is
$\Rightarrow 4x^2-16x+16=4(x+4)$
Factor out $4$ from the left hand side.
$\Rightarrow 4(x^2-4x+4)=4(x+4)$
Divide the equation by $4$.
$\Rightarrow \frac{4(x^2-4x+4)}{4}=\frac{4(x+4)}{4}$
Simplify.
$\Rightarrow x^2-4x+4=x+4$
Add $-x-4$ to both sides.
$\Rightarrow x^2-4x+4-x-4=x+4-x-4$
Add like terms.
$\Rightarrow x^2-5x=0$
Factor out $x$.
$\Rightarrow x(x-5)=0$
By using zero product rule set each factor equal to zero.
$\Rightarrow x=0$ or $x-5=0$
Isolate $x$.
$\Rightarrow x=0$ or $x=5$
The solution set is $\{0,5\}$.
