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Simplifying 4x = 12x + x2 + 15 Reorder the terms: 4x = 15 + 12x + x2 Solving 4x = 15 + 12x + x2 Solving for variable 'x'. Reorder the terms: -15 + 4x + -12x + -1x2 = 15 + 12x + x2 + -15 + -12x + -1x2 Combine like terms: 4x + -12x = -8x -15 + -8x + -1x2 = 15 + 12x + x2 + -15 + -12x + -1x2 Reorder the terms: -15 + -8x + -1x2 = 15 + -15 + 12x + -12x + x2 + -1x2 Combine like terms: 15 + -15 = 0 -15 + -8x + -1x2 = 0 + 12x + -12x + x2 + -1x2 -15 + -8x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -15 + -8x + -1x2 = 0 + x2 + -1x2 -15 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 8x + x2) = 0 Factor a trinomial. -1((5 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = {-5, -3}
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