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Simplifying 2(x + 2)(x + -3) + -8 = 4(x + 1)(x + -6) + 4 Reorder the terms: 2(2 + x)(x + -3) + -8 = 4(x + 1)(x + -6) + 4 Reorder the terms: 2(2 + x)(-3 + x) + -8 = 4(x + 1)(x + -6) + 4 Multiply (2 + x) * (-3 + x) 2(2(-3 + x) + x(-3 + x)) + -8 = 4(x + 1)(x + -6) + 4 2((-3 * 2 + x * 2) + x(-3 + x)) + -8 = 4(x + 1)(x + -6) + 4 2((-6 + 2x) + x(-3 + x)) + -8 = 4(x + 1)(x + -6) + 4 2(-6 + 2x + (-3 * x + x * x)) + -8 = 4(x + 1)(x + -6) + 4 2(-6 + 2x + (-3x + x2)) + -8 = 4(x + 1)(x + -6) + 4 Combine like terms: 2x + -3x = -1x 2(-6 + -1x + x2) + -8 = 4(x + 1)(x + -6) + 4 (-6 * 2 + -1x * 2 + x2 * 2) + -8 = 4(x + 1)(x + -6) + 4 (-12 + -2x + 2x2) + -8 = 4(x + 1)(x + -6) + 4 Reorder the terms: -12 + -8 + -2x + 2x2 = 4(x + 1)(x + -6) + 4 Combine like terms: -12 + -8 = -20 -20 + -2x + 2x2 = 4(x + 1)(x + -6) + 4 Reorder the terms: -20 + -2x + 2x2 = 4(1 + x)(x + -6) + 4 Reorder the terms: -20 + -2x + 2x2 = 4(1 + x)(-6 + x) + 4 Multiply (1 + x) * (-6 + x) -20 + -2x + 2x2 = 4(1(-6 + x) + x(-6 + x)) + 4 -20 + -2x + 2x2 = 4((-6 * 1 + x * 1) + x(-6 + x)) + 4 -20 + -2x + 2x2 = 4((-6 + 1x) + x(-6 + x)) + 4 -20 + -2x + 2x2 = 4(-6 + 1x + (-6 * x + x * x)) + 4 -20 + -2x + 2x2 = 4(-6 + 1x + (-6x + x2)) + 4 Combine like terms: 1x + -6x = -5x -20 + -2x + 2x2 = 4(-6 + -5x + x2) + 4 -20 + -2x + 2x2 = (-6 * 4 + -5x * 4 + x2 * 4) + 4 -20 + -2x + 2x2 = (-24 + -20x + 4x2) + 4 Reorder the terms: -20 + -2x + 2x2 = -24 + 4 + -20x + 4x2 Combine like terms: -24 + 4 = -20 -20 + -2x + 2x2 = -20 + -20x + 4x2 Add '20' to each side of the equation. -20 + -2x + 20 + 2x2 = -20 + -20x + 20 + 4x2 Reorder the terms: -20 + 20 + -2x + 2x2 = -20 + -20x + 20 + 4x2 Combine like terms: -20 + 20 = 0 0 + -2x + 2x2 = -20 + -20x + 20 + 4x2 -2x + 2x2 = -20 + -20x + 20 + 4x2 Reorder the terms: -2x + 2x2 = -20 + 20 + -20x + 4x2 Combine like terms: -20 + 20 = 0 -2x + 2x2 = 0 + -20x + 4x2 -2x + 2x2 = -20x + 4x2 Solving -2x + 2x2 = -20x + 4x2 Solving for variable 'x'. Reorder the terms: -2x + 20x + 2x2 + -4x2 = -20x + 4x2 + 20x + -4x2 Combine like terms: -2x + 20x = 18x 18x + 2x2 + -4x2 = -20x + 4x2 + 20x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 18x + -2x2 = -20x + 4x2 + 20x + -4x2 Reorder the terms: 18x + -2x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 18x + -2x2 = 0 + 4x2 + -4x2 18x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 18x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {0, 9}
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