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Simplifying (2x + -3)(x + 9) = (x + -9)(x + 3) Reorder the terms: (-3 + 2x)(x + 9) = (x + -9)(x + 3) Reorder the terms: (-3 + 2x)(9 + x) = (x + -9)(x + 3) Multiply (-3 + 2x) * (9 + x) (-3(9 + x) + 2x * (9 + x)) = (x + -9)(x + 3) ((9 * -3 + x * -3) + 2x * (9 + x)) = (x + -9)(x + 3) ((-27 + -3x) + 2x * (9 + x)) = (x + -9)(x + 3) (-27 + -3x + (9 * 2x + x * 2x)) = (x + -9)(x + 3) (-27 + -3x + (18x + 2x2)) = (x + -9)(x + 3) Combine like terms: -3x + 18x = 15x (-27 + 15x + 2x2) = (x + -9)(x + 3) Reorder the terms: -27 + 15x + 2x2 = (-9 + x)(x + 3) Reorder the terms: -27 + 15x + 2x2 = (-9 + x)(3 + x) Multiply (-9 + x) * (3 + x) -27 + 15x + 2x2 = (-9(3 + x) + x(3 + x)) -27 + 15x + 2x2 = ((3 * -9 + x * -9) + x(3 + x)) -27 + 15x + 2x2 = ((-27 + -9x) + x(3 + x)) -27 + 15x + 2x2 = (-27 + -9x + (3 * x + x * x)) -27 + 15x + 2x2 = (-27 + -9x + (3x + x2)) Combine like terms: -9x + 3x = -6x -27 + 15x + 2x2 = (-27 + -6x + x2) Add '27' to each side of the equation. -27 + 15x + 27 + 2x2 = -27 + -6x + 27 + x2 Reorder the terms: -27 + 27 + 15x + 2x2 = -27 + -6x + 27 + x2 Combine like terms: -27 + 27 = 0 0 + 15x + 2x2 = -27 + -6x + 27 + x2 15x + 2x2 = -27 + -6x + 27 + x2 Reorder the terms: 15x + 2x2 = -27 + 27 + -6x + x2 Combine like terms: -27 + 27 = 0 15x + 2x2 = 0 + -6x + x2 15x + 2x2 = -6x + x2 Solving 15x + 2x2 = -6x + x2 Solving for variable 'x'. Reorder the terms: 15x + 6x + 2x2 + -1x2 = -6x + x2 + 6x + -1x2 Combine like terms: 15x + 6x = 21x 21x + 2x2 + -1x2 = -6x + x2 + 6x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 21x + 1x2 = -6x + x2 + 6x + -1x2 Reorder the terms: 21x + 1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 21x + 1x2 = 0 + x2 + -1x2 21x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(21 + 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 '(21 + x)' equal to zero and attempt to solve: Simplifying 21 + x = 0 Solving 21 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + x = 0 + -21 x = 0 + -21 Combine like terms: 0 + -21 = -21 x = -21 Simplifying x = -21Solution
x = {0, -21}
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