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Simplifying (2x + -3)(2x + 3) = (x + -1)(x + 1) + (5x + 2)(x + -4) Reorder the terms: (-3 + 2x)(2x + 3) = (x + -1)(x + 1) + (5x + 2)(x + -4) Reorder the terms: (-3 + 2x)(3 + 2x) = (x + -1)(x + 1) + (5x + 2)(x + -4) Multiply (-3 + 2x) * (3 + 2x) (-3(3 + 2x) + 2x * (3 + 2x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) ((3 * -3 + 2x * -3) + 2x * (3 + 2x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) ((-9 + -6x) + 2x * (3 + 2x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) (-9 + -6x + (3 * 2x + 2x * 2x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) (-9 + -6x + (6x + 4x2)) = (x + -1)(x + 1) + (5x + 2)(x + -4) Combine like terms: -6x + 6x = 0 (-9 + 0 + 4x2) = (x + -1)(x + 1) + (5x + 2)(x + -4) (-9 + 4x2) = (x + -1)(x + 1) + (5x + 2)(x + -4) Reorder the terms: -9 + 4x2 = (-1 + x)(x + 1) + (5x + 2)(x + -4) Reorder the terms: -9 + 4x2 = (-1 + x)(1 + x) + (5x + 2)(x + -4) Multiply (-1 + x) * (1 + x) -9 + 4x2 = (-1(1 + x) + x(1 + x)) + (5x + 2)(x + -4) -9 + 4x2 = ((1 * -1 + x * -1) + x(1 + x)) + (5x + 2)(x + -4) -9 + 4x2 = ((-1 + -1x) + x(1 + x)) + (5x + 2)(x + -4) -9 + 4x2 = (-1 + -1x + (1 * x + x * x)) + (5x + 2)(x + -4) -9 + 4x2 = (-1 + -1x + (1x + x2)) + (5x + 2)(x + -4) Combine like terms: -1x + 1x = 0 -9 + 4x2 = (-1 + 0 + x2) + (5x + 2)(x + -4) -9 + 4x2 = (-1 + x2) + (5x + 2)(x + -4) Reorder the terms: -9 + 4x2 = -1 + x2 + (2 + 5x)(x + -4) Reorder the terms: -9 + 4x2 = -1 + x2 + (2 + 5x)(-4 + x) Multiply (2 + 5x) * (-4 + x) -9 + 4x2 = -1 + x2 + (2(-4 + x) + 5x * (-4 + x)) -9 + 4x2 = -1 + x2 + ((-4 * 2 + x * 2) + 5x * (-4 + x)) -9 + 4x2 = -1 + x2 + ((-8 + 2x) + 5x * (-4 + x)) -9 + 4x2 = -1 + x2 + (-8 + 2x + (-4 * 5x + x * 5x)) -9 + 4x2 = -1 + x2 + (-8 + 2x + (-20x + 5x2)) Combine like terms: 2x + -20x = -18x -9 + 4x2 = -1 + x2 + (-8 + -18x + 5x2) Reorder the terms: -9 + 4x2 = -1 + -8 + -18x + x2 + 5x2 Combine like terms: -1 + -8 = -9 -9 + 4x2 = -9 + -18x + x2 + 5x2 Combine like terms: x2 + 5x2 = 6x2 -9 + 4x2 = -9 + -18x + 6x2 Add '9' to each side of the equation. -9 + 9 + 4x2 = -9 + -18x + 9 + 6x2 Combine like terms: -9 + 9 = 0 0 + 4x2 = -9 + -18x + 9 + 6x2 4x2 = -9 + -18x + 9 + 6x2 Reorder the terms: 4x2 = -9 + 9 + -18x + 6x2 Combine like terms: -9 + 9 = 0 4x2 = 0 + -18x + 6x2 4x2 = -18x + 6x2 Solving 4x2 = -18x + 6x2 Solving for variable 'x'. Reorder the terms: 18x + 4x2 + -6x2 = -18x + 6x2 + 18x + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 18x + -2x2 = -18x + 6x2 + 18x + -6x2 Reorder the terms: 18x + -2x2 = -18x + 18x + 6x2 + -6x2 Combine like terms: -18x + 18x = 0 18x + -2x2 = 0 + 6x2 + -6x2 18x + -2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 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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