How do you find the values that $x$ can take by squaring? $$|x+4| \cdot |x-4| = x+4$$
How do you find the values that $x$ can take by squaring? 
How I've tried
$$|x+4|^2 \cdot |x-4|^2 = (x+4)^2$$
and
$$|x^2+16| \cdot |x^2+16| = x^2+16$$
I think I went wrong. 

Do squaring!
$$ (\vert x- 4 \vert \cdot \vert x + 4 \vert)^2 = (x + 4)^2 $$
$$ (\vert x- 4 \vert)^2 \cdot (\vert x + 4 \vert)^2 = (x + 4)^2 $$
$$ (x- 4)^2 \cdot ( x + 4)^2 = (x + 4)^2 $$
$$ (x- 4)^2 \cdot ( x + 4)^2 - (x + 4)^2=0 $$
$$ (x + 4)^2  \left[(x - 4)^2 - 1\right] =0 $$
$$ (x+4)^2=0, (x-4)^2 - 1 = 0$$
$$\implies x= -4, x = 4±\sqrt{1}$$
$$\implies x= -4, x = 5,x= 3$$

Njoy!
