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Simplifying 6x2 + 15x + -135 = -12x Reorder the terms: -135 + 15x + 6x2 = -12x Solving -135 + 15x + 6x2 = -12x Solving for variable 'x'. Reorder the terms: -135 + 15x + 12x + 6x2 = -12x + 12x Combine like terms: 15x + 12x = 27x -135 + 27x + 6x2 = -12x + 12x Combine like terms: -12x + 12x = 0 -135 + 27x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-45 + 9x + 2x2) = 0 Factor a trinomial. 3((-15 + -2x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve: Simplifying -15 + -2x = 0 Solving -15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2x = 0 + 15 -2x = 0 + 15 Combine like terms: 0 + 15 = 15 -2x = 15 Divide each side by '-2'. x = -7.5 Simplifying x = -7.5Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-7.5, 3}
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