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Simplifying (x + -5)(2x + 4) = (x + 5)(x + -4) Reorder the terms: (-5 + x)(2x + 4) = (x + 5)(x + -4) Reorder the terms: (-5 + x)(4 + 2x) = (x + 5)(x + -4) Multiply (-5 + x) * (4 + 2x) (-5(4 + 2x) + x(4 + 2x)) = (x + 5)(x + -4) ((4 * -5 + 2x * -5) + x(4 + 2x)) = (x + 5)(x + -4) ((-20 + -10x) + x(4 + 2x)) = (x + 5)(x + -4) (-20 + -10x + (4 * x + 2x * x)) = (x + 5)(x + -4) (-20 + -10x + (4x + 2x2)) = (x + 5)(x + -4) Combine like terms: -10x + 4x = -6x (-20 + -6x + 2x2) = (x + 5)(x + -4) Reorder the terms: -20 + -6x + 2x2 = (5 + x)(x + -4) Reorder the terms: -20 + -6x + 2x2 = (5 + x)(-4 + x) Multiply (5 + x) * (-4 + x) -20 + -6x + 2x2 = (5(-4 + x) + x(-4 + x)) -20 + -6x + 2x2 = ((-4 * 5 + x * 5) + x(-4 + x)) -20 + -6x + 2x2 = ((-20 + 5x) + x(-4 + x)) -20 + -6x + 2x2 = (-20 + 5x + (-4 * x + x * x)) -20 + -6x + 2x2 = (-20 + 5x + (-4x + x2)) Combine like terms: 5x + -4x = 1x -20 + -6x + 2x2 = (-20 + 1x + x2) Add '20' to each side of the equation. -20 + -6x + 20 + 2x2 = -20 + 1x + 20 + x2 Reorder the terms: -20 + 20 + -6x + 2x2 = -20 + 1x + 20 + x2 Combine like terms: -20 + 20 = 0 0 + -6x + 2x2 = -20 + 1x + 20 + x2 -6x + 2x2 = -20 + 1x + 20 + x2 Reorder the terms: -6x + 2x2 = -20 + 20 + 1x + x2 Combine like terms: -20 + 20 = 0 -6x + 2x2 = 0 + 1x + x2 -6x + 2x2 = 1x + x2 Solving -6x + 2x2 = 1x + x2 Solving for variable 'x'. Reorder the terms: -6x + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: -6x + -1x = -7x -7x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -7x + 1x2 = 1x + x2 + -1x + -1x2 Reorder the terms: -7x + 1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 -7x + 1x2 = 0 + x2 + -1x2 -7x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Solution
x = {0, 7}
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