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Simplifying (x + 2)(x + 3) = (3x + 4)(x + 3) Reorder the terms: (2 + x)(x + 3) = (3x + 4)(x + 3) Reorder the terms: (2 + x)(3 + x) = (3x + 4)(x + 3) Multiply (2 + x) * (3 + x) (2(3 + x) + x(3 + x)) = (3x + 4)(x + 3) ((3 * 2 + x * 2) + x(3 + x)) = (3x + 4)(x + 3) ((6 + 2x) + x(3 + x)) = (3x + 4)(x + 3) (6 + 2x + (3 * x + x * x)) = (3x + 4)(x + 3) (6 + 2x + (3x + x2)) = (3x + 4)(x + 3) Combine like terms: 2x + 3x = 5x (6 + 5x + x2) = (3x + 4)(x + 3) Reorder the terms: 6 + 5x + x2 = (4 + 3x)(x + 3) Reorder the terms: 6 + 5x + x2 = (4 + 3x)(3 + x) Multiply (4 + 3x) * (3 + x) 6 + 5x + x2 = (4(3 + x) + 3x * (3 + x)) 6 + 5x + x2 = ((3 * 4 + x * 4) + 3x * (3 + x)) 6 + 5x + x2 = ((12 + 4x) + 3x * (3 + x)) 6 + 5x + x2 = (12 + 4x + (3 * 3x + x * 3x)) 6 + 5x + x2 = (12 + 4x + (9x + 3x2)) Combine like terms: 4x + 9x = 13x 6 + 5x + x2 = (12 + 13x + 3x2) Solving 6 + 5x + x2 = 12 + 13x + 3x2 Solving for variable 'x'. Reorder the terms: 6 + -12 + 5x + -13x + x2 + -3x2 = 12 + 13x + 3x2 + -12 + -13x + -3x2 Combine like terms: 6 + -12 = -6 -6 + 5x + -13x + x2 + -3x2 = 12 + 13x + 3x2 + -12 + -13x + -3x2 Combine like terms: 5x + -13x = -8x -6 + -8x + x2 + -3x2 = 12 + 13x + 3x2 + -12 + -13x + -3x2 Combine like terms: x2 + -3x2 = -2x2 -6 + -8x + -2x2 = 12 + 13x + 3x2 + -12 + -13x + -3x2 Reorder the terms: -6 + -8x + -2x2 = 12 + -12 + 13x + -13x + 3x2 + -3x2 Combine like terms: 12 + -12 = 0 -6 + -8x + -2x2 = 0 + 13x + -13x + 3x2 + -3x2 -6 + -8x + -2x2 = 13x + -13x + 3x2 + -3x2 Combine like terms: 13x + -13x = 0 -6 + -8x + -2x2 = 0 + 3x2 + -3x2 -6 + -8x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 4x + x2) = 0 Factor a trinomial. -2((3 + x)(1 + x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-3, -1}
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