Question

question
solve for all values of ( x ) by factoring.
( x^2 - 5x - 12 = -5x + 4 )

Explanation:

Step1: Simplify the equation

Add $5x$ to both sides:
$x^2 - 5x - 12 + 5x = -5x + 4 + 5x$
$x^2 - 12 = 4$

Step2: Isolate the quadratic term

Add 12 to both sides:
$x^2 - 12 + 12 = 4 + 12$
$x^2 = 16$

Step3: Factor as difference of squares

Rewrite 16 as $4^2$, then factor:
$x^2 - 4^2 = 0$
$(x - 4)(x + 4) = 0$

Step4: Solve for $x$

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

Answer:

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