(x+6)(2x-8)=1008

Solution for (x+6)(2x-8)=1008 equation:

Simplifying
(x + 6)(2x + -8) = 1008

Reorder the terms:
(6 + x)(2x + -8) = 1008

Reorder the terms:
(6 + x)(-8 + 2x) = 1008

Multiply (6 + x) * (-8 + 2x)
(6(-8 + 2x) + x(-8 + 2x)) = 1008
((-8 * 6 + 2x * 6) + x(-8 + 2x)) = 1008
((-48 + 12x) + x(-8 + 2x)) = 1008
(-48 + 12x + (-8 * x + 2x * x)) = 1008
(-48 + 12x + (-8x + 2x2)) = 1008

Combine like terms: 12x + -8x = 4x
(-48 + 4x + 2x2) = 1008

Solving
-48 + 4x + 2x2 = 1008

Solving for variable 'x'.

Reorder the terms:
-48 + -1008 + 4x + 2x2 = 1008 + -1008

Combine like terms: -48 + -1008 = -1056
-1056 + 4x + 2x2 = 1008 + -1008

Combine like terms: 1008 + -1008 = 0
-1056 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-528 + 2x + x2) = 0

Factor a trinomial.
2((-24 + -1x)(22 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-24, 22}