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