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Simplifying (3x + 4)(x + 9) = (4x + 3)(x + 12) Reorder the terms: (4 + 3x)(x + 9) = (4x + 3)(x + 12) Reorder the terms: (4 + 3x)(9 + x) = (4x + 3)(x + 12) Multiply (4 + 3x) * (9 + x) (4(9 + x) + 3x * (9 + x)) = (4x + 3)(x + 12) ((9 * 4 + x * 4) + 3x * (9 + x)) = (4x + 3)(x + 12) ((36 + 4x) + 3x * (9 + x)) = (4x + 3)(x + 12) (36 + 4x + (9 * 3x + x * 3x)) = (4x + 3)(x + 12) (36 + 4x + (27x + 3x2)) = (4x + 3)(x + 12) Combine like terms: 4x + 27x = 31x (36 + 31x + 3x2) = (4x + 3)(x + 12) Reorder the terms: 36 + 31x + 3x2 = (3 + 4x)(x + 12) Reorder the terms: 36 + 31x + 3x2 = (3 + 4x)(12 + x) Multiply (3 + 4x) * (12 + x) 36 + 31x + 3x2 = (3(12 + x) + 4x * (12 + x)) 36 + 31x + 3x2 = ((12 * 3 + x * 3) + 4x * (12 + x)) 36 + 31x + 3x2 = ((36 + 3x) + 4x * (12 + x)) 36 + 31x + 3x2 = (36 + 3x + (12 * 4x + x * 4x)) 36 + 31x + 3x2 = (36 + 3x + (48x + 4x2)) Combine like terms: 3x + 48x = 51x 36 + 31x + 3x2 = (36 + 51x + 4x2) Add '-36' to each side of the equation. 36 + 31x + -36 + 3x2 = 36 + 51x + -36 + 4x2 Reorder the terms: 36 + -36 + 31x + 3x2 = 36 + 51x + -36 + 4x2 Combine like terms: 36 + -36 = 0 0 + 31x + 3x2 = 36 + 51x + -36 + 4x2 31x + 3x2 = 36 + 51x + -36 + 4x2 Reorder the terms: 31x + 3x2 = 36 + -36 + 51x + 4x2 Combine like terms: 36 + -36 = 0 31x + 3x2 = 0 + 51x + 4x2 31x + 3x2 = 51x + 4x2 Solving 31x + 3x2 = 51x + 4x2 Solving for variable 'x'. Reorder the terms: 31x + -51x + 3x2 + -4x2 = 51x + 4x2 + -51x + -4x2 Combine like terms: 31x + -51x = -20x -20x + 3x2 + -4x2 = 51x + 4x2 + -51x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 -20x + -1x2 = 51x + 4x2 + -51x + -4x2 Reorder the terms: -20x + -1x2 = 51x + -51x + 4x2 + -4x2 Combine like terms: 51x + -51x = 0 -20x + -1x2 = 0 + 4x2 + -4x2 -20x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(20 + x) = 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 '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20Solution
x = {0, -20}
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