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

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


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

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

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

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

Combine like terms: -8x + 12x = 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}

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