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Simplifying -6x2 + -65x + -135 = -3x2 + -38x + -75 Reorder the terms: -135 + -65x + -6x2 = -3x2 + -38x + -75 Reorder the terms: -135 + -65x + -6x2 = -75 + -38x + -3x2 Solving -135 + -65x + -6x2 = -75 + -38x + -3x2 Solving for variable 'x'. Reorder the terms: -135 + 75 + -65x + 38x + -6x2 + 3x2 = -75 + -38x + -3x2 + 75 + 38x + 3x2 Combine like terms: -135 + 75 = -60 -60 + -65x + 38x + -6x2 + 3x2 = -75 + -38x + -3x2 + 75 + 38x + 3x2 Combine like terms: -65x + 38x = -27x -60 + -27x + -6x2 + 3x2 = -75 + -38x + -3x2 + 75 + 38x + 3x2 Combine like terms: -6x2 + 3x2 = -3x2 -60 + -27x + -3x2 = -75 + -38x + -3x2 + 75 + 38x + 3x2 Reorder the terms: -60 + -27x + -3x2 = -75 + 75 + -38x + 38x + -3x2 + 3x2 Combine like terms: -75 + 75 = 0 -60 + -27x + -3x2 = 0 + -38x + 38x + -3x2 + 3x2 -60 + -27x + -3x2 = -38x + 38x + -3x2 + 3x2 Combine like terms: -38x + 38x = 0 -60 + -27x + -3x2 = 0 + -3x2 + 3x2 -60 + -27x + -3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -60 + -27x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(20 + 9x + x2) = 0 Factor a trinomial. -3((5 + x)(4 + x)) = 0 Ignore the factor -3.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-5, -4}
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