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Simplifying (x + -6)(2x + 5) = (x + 6)(x + -5) Reorder the terms: (-6 + x)(2x + 5) = (x + 6)(x + -5) Reorder the terms: (-6 + x)(5 + 2x) = (x + 6)(x + -5) Multiply (-6 + x) * (5 + 2x) (-6(5 + 2x) + x(5 + 2x)) = (x + 6)(x + -5) ((5 * -6 + 2x * -6) + x(5 + 2x)) = (x + 6)(x + -5) ((-30 + -12x) + x(5 + 2x)) = (x + 6)(x + -5) (-30 + -12x + (5 * x + 2x * x)) = (x + 6)(x + -5) (-30 + -12x + (5x + 2x2)) = (x + 6)(x + -5) Combine like terms: -12x + 5x = -7x (-30 + -7x + 2x2) = (x + 6)(x + -5) Reorder the terms: -30 + -7x + 2x2 = (6 + x)(x + -5) Reorder the terms: -30 + -7x + 2x2 = (6 + x)(-5 + x) Multiply (6 + x) * (-5 + x) -30 + -7x + 2x2 = (6(-5 + x) + x(-5 + x)) -30 + -7x + 2x2 = ((-5 * 6 + x * 6) + x(-5 + x)) -30 + -7x + 2x2 = ((-30 + 6x) + x(-5 + x)) -30 + -7x + 2x2 = (-30 + 6x + (-5 * x + x * x)) -30 + -7x + 2x2 = (-30 + 6x + (-5x + x2)) Combine like terms: 6x + -5x = 1x -30 + -7x + 2x2 = (-30 + 1x + x2) Add '30' to each side of the equation. -30 + -7x + 30 + 2x2 = -30 + 1x + 30 + x2 Reorder the terms: -30 + 30 + -7x + 2x2 = -30 + 1x + 30 + x2 Combine like terms: -30 + 30 = 0 0 + -7x + 2x2 = -30 + 1x + 30 + x2 -7x + 2x2 = -30 + 1x + 30 + x2 Reorder the terms: -7x + 2x2 = -30 + 30 + 1x + x2 Combine like terms: -30 + 30 = 0 -7x + 2x2 = 0 + 1x + x2 -7x + 2x2 = 1x + x2 Solving -7x + 2x2 = 1x + x2 Solving for variable 'x'. Reorder the terms: -7x + -1x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: -7x + -1x = -8x -8x + 2x2 + -1x2 = 1x + x2 + -1x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -8x + 1x2 = 1x + x2 + -1x + -1x2 Reorder the terms: -8x + 1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 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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