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Simplifying (2x + -3)(x + 9) = (x + -3)(x + 9) Reorder the terms: (-3 + 2x)(x + 9) = (x + -3)(x + 9) Reorder the terms: (-3 + 2x)(9 + x) = (x + -3)(x + 9) Multiply (-3 + 2x) * (9 + x) (-3(9 + x) + 2x * (9 + x)) = (x + -3)(x + 9) ((9 * -3 + x * -3) + 2x * (9 + x)) = (x + -3)(x + 9) ((-27 + -3x) + 2x * (9 + x)) = (x + -3)(x + 9) (-27 + -3x + (9 * 2x + x * 2x)) = (x + -3)(x + 9) (-27 + -3x + (18x + 2x2)) = (x + -3)(x + 9) Combine like terms: -3x + 18x = 15x (-27 + 15x + 2x2) = (x + -3)(x + 9) Reorder the terms: -27 + 15x + 2x2 = (-3 + x)(x + 9) Reorder the terms: -27 + 15x + 2x2 = (-3 + x)(9 + x) Multiply (-3 + x) * (9 + x) -27 + 15x + 2x2 = (-3(9 + x) + x(9 + x)) -27 + 15x + 2x2 = ((9 * -3 + x * -3) + x(9 + x)) -27 + 15x + 2x2 = ((-27 + -3x) + x(9 + x)) -27 + 15x + 2x2 = (-27 + -3x + (9 * x + x * x)) -27 + 15x + 2x2 = (-27 + -3x + (9x + x2)) Combine like terms: -3x + 9x = 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 = 9x 9x + 2x2 + -1x2 = 6x + x2 + -6x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 9x + 1x2 = 6x + x2 + -6x + -1x2 Reorder the terms: 9x + 1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 9x + 1x2 = 0 + x2 + -1x2 9x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(9 + 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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Solution
x = {0, -9}
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