Question

solve for all values of x by factoring. x² - 4x - 16 = -4x

Explanation:

Step1: Simplify the equation

Add $4x$ to both sides.
$x^2 - 4x - 16 + 4x = -4x + 4x$
Simplify to get $x^2 - 16 = 0$

Step2: Factor the quadratic

Rewrite as difference of squares.
$x^2 - 4^2 = 0$
Factor into $(x-4)(x+4) = 0$

Step3: Solve for $x$

Set each factor equal to 0.
$x-4=0$ or $x+4=0$

Answer:

$x=4$ and $x=-4$