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Simplifying (2x + 2)(2x + -4) = (x + 4)(2x + -2) Reorder the terms: (2 + 2x)(2x + -4) = (x + 4)(2x + -2) Reorder the terms: (2 + 2x)(-4 + 2x) = (x + 4)(2x + -2) Multiply (2 + 2x) * (-4 + 2x) (2(-4 + 2x) + 2x * (-4 + 2x)) = (x + 4)(2x + -2) ((-4 * 2 + 2x * 2) + 2x * (-4 + 2x)) = (x + 4)(2x + -2) ((-8 + 4x) + 2x * (-4 + 2x)) = (x + 4)(2x + -2) (-8 + 4x + (-4 * 2x + 2x * 2x)) = (x + 4)(2x + -2) (-8 + 4x + (-8x + 4x2)) = (x + 4)(2x + -2) Combine like terms: 4x + -8x = -4x (-8 + -4x + 4x2) = (x + 4)(2x + -2) Reorder the terms: -8 + -4x + 4x2 = (4 + x)(2x + -2) Reorder the terms: -8 + -4x + 4x2 = (4 + x)(-2 + 2x) Multiply (4 + x) * (-2 + 2x) -8 + -4x + 4x2 = (4(-2 + 2x) + x(-2 + 2x)) -8 + -4x + 4x2 = ((-2 * 4 + 2x * 4) + x(-2 + 2x)) -8 + -4x + 4x2 = ((-8 + 8x) + x(-2 + 2x)) -8 + -4x + 4x2 = (-8 + 8x + (-2 * x + 2x * x)) -8 + -4x + 4x2 = (-8 + 8x + (-2x + 2x2)) Combine like terms: 8x + -2x = 6x -8 + -4x + 4x2 = (-8 + 6x + 2x2) Add '8' to each side of the equation. -8 + -4x + 8 + 4x2 = -8 + 6x + 8 + 2x2 Reorder the terms: -8 + 8 + -4x + 4x2 = -8 + 6x + 8 + 2x2 Combine like terms: -8 + 8 = 0 0 + -4x + 4x2 = -8 + 6x + 8 + 2x2 -4x + 4x2 = -8 + 6x + 8 + 2x2 Reorder the terms: -4x + 4x2 = -8 + 8 + 6x + 2x2 Combine like terms: -8 + 8 = 0 -4x + 4x2 = 0 + 6x + 2x2 -4x + 4x2 = 6x + 2x2 Solving -4x + 4x2 = 6x + 2x2 Solving for variable 'x'. Reorder the terms: -4x + -6x + 4x2 + -2x2 = 6x + 2x2 + -6x + -2x2 Combine like terms: -4x + -6x = -10x -10x + 4x2 + -2x2 = 6x + 2x2 + -6x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 -10x + 2x2 = 6x + 2x2 + -6x + -2x2 Reorder the terms: -10x + 2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -10x + 2x2 = 0 + 2x2 + -2x2 -10x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + x) = 0 Ignore the factor 2.Subproblem 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Solution
x = {0, 5}
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