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Simplifying 2x + 6 = (x + 5)(x + 3) Reorder the terms: 6 + 2x = (x + 5)(x + 3) Reorder the terms: 6 + 2x = (5 + x)(x + 3) Reorder the terms: 6 + 2x = (5 + x)(3 + x) Multiply (5 + x) * (3 + x) 6 + 2x = (5(3 + x) + x(3 + x)) 6 + 2x = ((3 * 5 + x * 5) + x(3 + x)) 6 + 2x = ((15 + 5x) + x(3 + x)) 6 + 2x = (15 + 5x + (3 * x + x * x)) 6 + 2x = (15 + 5x + (3x + x2)) Combine like terms: 5x + 3x = 8x 6 + 2x = (15 + 8x + x2) Solving 6 + 2x = 15 + 8x + x2 Solving for variable 'x'. Reorder the terms: 6 + -15 + 2x + -8x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2 Combine like terms: 6 + -15 = -9 -9 + 2x + -8x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2 Combine like terms: 2x + -8x = -6x -9 + -6x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2 Reorder the terms: -9 + -6x + -1x2 = 15 + -15 + 8x + -8x + x2 + -1x2 Combine like terms: 15 + -15 = 0 -9 + -6x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -9 + -6x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -9 + -6x + -1x2 = 0 + x2 + -1x2 -9 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 6x + x2) = 0 Factor a trinomial. -1((3 + x)(3 + x)) = 0 Ignore the factor -1.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 '(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 = -3Solution
x = {-3, -3}
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