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Simplifying (2x + 6)(2x + -6) = (2x + 9)(3x + -4) Reorder the terms: (6 + 2x)(2x + -6) = (2x + 9)(3x + -4) Reorder the terms: (6 + 2x)(-6 + 2x) = (2x + 9)(3x + -4) Multiply (6 + 2x) * (-6 + 2x) (6(-6 + 2x) + 2x * (-6 + 2x)) = (2x + 9)(3x + -4) ((-6 * 6 + 2x * 6) + 2x * (-6 + 2x)) = (2x + 9)(3x + -4) ((-36 + 12x) + 2x * (-6 + 2x)) = (2x + 9)(3x + -4) (-36 + 12x + (-6 * 2x + 2x * 2x)) = (2x + 9)(3x + -4) (-36 + 12x + (-12x + 4x2)) = (2x + 9)(3x + -4) Combine like terms: 12x + -12x = 0 (-36 + 0 + 4x2) = (2x + 9)(3x + -4) (-36 + 4x2) = (2x + 9)(3x + -4) Reorder the terms: -36 + 4x2 = (9 + 2x)(3x + -4) Reorder the terms: -36 + 4x2 = (9 + 2x)(-4 + 3x) Multiply (9 + 2x) * (-4 + 3x) -36 + 4x2 = (9(-4 + 3x) + 2x * (-4 + 3x)) -36 + 4x2 = ((-4 * 9 + 3x * 9) + 2x * (-4 + 3x)) -36 + 4x2 = ((-36 + 27x) + 2x * (-4 + 3x)) -36 + 4x2 = (-36 + 27x + (-4 * 2x + 3x * 2x)) -36 + 4x2 = (-36 + 27x + (-8x + 6x2)) Combine like terms: 27x + -8x = 19x -36 + 4x2 = (-36 + 19x + 6x2) Add '36' to each side of the equation. -36 + 36 + 4x2 = -36 + 19x + 36 + 6x2 Combine like terms: -36 + 36 = 0 0 + 4x2 = -36 + 19x + 36 + 6x2 4x2 = -36 + 19x + 36 + 6x2 Reorder the terms: 4x2 = -36 + 36 + 19x + 6x2 Combine like terms: -36 + 36 = 0 4x2 = 0 + 19x + 6x2 4x2 = 19x + 6x2 Solving 4x2 = 19x + 6x2 Solving for variable 'x'. Reorder the terms: -19x + 4x2 + -6x2 = 19x + 6x2 + -19x + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 -19x + -2x2 = 19x + 6x2 + -19x + -6x2 Reorder the terms: -19x + -2x2 = 19x + -19x + 6x2 + -6x2 Combine like terms: 19x + -19x = 0 -19x + -2x2 = 0 + 6x2 + -6x2 -19x + -2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -19x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(19 + 2x) = 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 '(19 + 2x)' equal to zero and attempt to solve: Simplifying 19 + 2x = 0 Solving 19 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 2x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 2x = 0 + -19 2x = 0 + -19 Combine like terms: 0 + -19 = -19 2x = -19 Divide each side by '2'. x = -9.5 Simplifying x = -9.5Solution
x = {0, -9.5}
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