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Simplifying (x + -4)(2x + 2) = (x + 4)(x + -2) Reorder the terms: (-4 + x)(2x + 2) = (x + 4)(x + -2) Reorder the terms: (-4 + x)(2 + 2x) = (x + 4)(x + -2) Multiply (-4 + x) * (2 + 2x) (-4(2 + 2x) + x(2 + 2x)) = (x + 4)(x + -2) ((2 * -4 + 2x * -4) + x(2 + 2x)) = (x + 4)(x + -2) ((-8 + -8x) + x(2 + 2x)) = (x + 4)(x + -2) (-8 + -8x + (2 * x + 2x * x)) = (x + 4)(x + -2) (-8 + -8x + (2x + 2x2)) = (x + 4)(x + -2) Combine like terms: -8x + 2x = -6x (-8 + -6x + 2x2) = (x + 4)(x + -2) Reorder the terms: -8 + -6x + 2x2 = (4 + x)(x + -2) Reorder the terms: -8 + -6x + 2x2 = (4 + x)(-2 + x) Multiply (4 + x) * (-2 + x) -8 + -6x + 2x2 = (4(-2 + x) + x(-2 + x)) -8 + -6x + 2x2 = ((-2 * 4 + x * 4) + x(-2 + x)) -8 + -6x + 2x2 = ((-8 + 4x) + x(-2 + x)) -8 + -6x + 2x2 = (-8 + 4x + (-2 * x + x * x)) -8 + -6x + 2x2 = (-8 + 4x + (-2x + x2)) Combine like terms: 4x + -2x = 2x -8 + -6x + 2x2 = (-8 + 2x + x2) Add '8' to each side of the equation. -8 + -6x + 8 + 2x2 = -8 + 2x + 8 + x2 Reorder the terms: -8 + 8 + -6x + 2x2 = -8 + 2x + 8 + x2 Combine like terms: -8 + 8 = 0 0 + -6x + 2x2 = -8 + 2x + 8 + x2 -6x + 2x2 = -8 + 2x + 8 + x2 Reorder the terms: -6x + 2x2 = -8 + 8 + 2x + x2 Combine like terms: -8 + 8 = 0 -6x + 2x2 = 0 + 2x + x2 -6x + 2x2 = 2x + x2 Solving -6x + 2x2 = 2x + x2 Solving for variable 'x'. Reorder the terms: -6x + -2x + 2x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: -6x + -2x = -8x -8x + 2x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -8x + 1x2 = 2x + x2 + -2x + -1x2 Reorder the terms: -8x + 1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -8x + 1x2 = 0 + x2 + -1x2 -8x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Solution
x = {0, 8}
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