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