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Simplifying (x + -7) * x(x + -2) = (x + -4) * x(x + -4) Reorder the terms: (-7 + x) * x(x + -2) = (x + -4) * x(x + -4) Reorder the terms: (-7 + x) * x(-2 + x) = (x + -4) * x(x + -4) Reorder the terms for easier multiplication: x(-7 + x)(-2 + x) = (x + -4) * x(x + -4) Multiply (-7 + x) * (-2 + x) x(-7(-2 + x) + x(-2 + x)) = (x + -4) * x(x + -4) x((-2 * -7 + x * -7) + x(-2 + x)) = (x + -4) * x(x + -4) x((14 + -7x) + x(-2 + x)) = (x + -4) * x(x + -4) x(14 + -7x + (-2 * x + x * x)) = (x + -4) * x(x + -4) x(14 + -7x + (-2x + x2)) = (x + -4) * x(x + -4) Combine like terms: -7x + -2x = -9x x(14 + -9x + x2) = (x + -4) * x(x + -4) (14 * x + -9x * x + x2 * x) = (x + -4) * x(x + -4) (14x + -9x2 + x3) = (x + -4) * x(x + -4) Reorder the terms: 14x + -9x2 + x3 = (-4 + x) * x(x + -4) Reorder the terms: 14x + -9x2 + x3 = (-4 + x) * x(-4 + x) Reorder the terms for easier multiplication: 14x + -9x2 + x3 = x(-4 + x)(-4 + x) Multiply (-4 + x) * (-4 + x) 14x + -9x2 + x3 = x(-4(-4 + x) + x(-4 + x)) 14x + -9x2 + x3 = x((-4 * -4 + x * -4) + x(-4 + x)) 14x + -9x2 + x3 = x((16 + -4x) + x(-4 + x)) 14x + -9x2 + x3 = x(16 + -4x + (-4 * x + x * x)) 14x + -9x2 + x3 = x(16 + -4x + (-4x + x2)) Combine like terms: -4x + -4x = -8x 14x + -9x2 + x3 = x(16 + -8x + x2) 14x + -9x2 + x3 = (16 * x + -8x * x + x2 * x) 14x + -9x2 + x3 = (16x + -8x2 + x3) Add '-1x3' to each side of the equation. 14x + -9x2 + x3 + -1x3 = 16x + -8x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 14x + -9x2 + 0 = 16x + -8x2 + x3 + -1x3 14x + -9x2 = 16x + -8x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 14x + -9x2 = 16x + -8x2 + 0 14x + -9x2 = 16x + -8x2 Solving 14x + -9x2 = 16x + -8x2 Solving for variable 'x'. Reorder the terms: 14x + -16x + -9x2 + 8x2 = 16x + -8x2 + -16x + 8x2 Combine like terms: 14x + -16x = -2x -2x + -9x2 + 8x2 = 16x + -8x2 + -16x + 8x2 Combine like terms: -9x2 + 8x2 = -1x2 -2x + -1x2 = 16x + -8x2 + -16x + 8x2 Reorder the terms: -2x + -1x2 = 16x + -16x + -8x2 + 8x2 Combine like terms: 16x + -16x = 0 -2x + -1x2 = 0 + -8x2 + 8x2 -2x + -1x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -2x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(2 + x) = 0 Ignore the factor -1.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, -2}
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