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