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Simplifying 15x2 + -107x + -368 = 11x2 + -51x + 12 Reorder the terms: -368 + -107x + 15x2 = 11x2 + -51x + 12 Reorder the terms: -368 + -107x + 15x2 = 12 + -51x + 11x2 Solving -368 + -107x + 15x2 = 12 + -51x + 11x2 Solving for variable 'x'. Reorder the terms: -368 + -12 + -107x + 51x + 15x2 + -11x2 = 12 + -51x + 11x2 + -12 + 51x + -11x2 Combine like terms: -368 + -12 = -380 -380 + -107x + 51x + 15x2 + -11x2 = 12 + -51x + 11x2 + -12 + 51x + -11x2 Combine like terms: -107x + 51x = -56x -380 + -56x + 15x2 + -11x2 = 12 + -51x + 11x2 + -12 + 51x + -11x2 Combine like terms: 15x2 + -11x2 = 4x2 -380 + -56x + 4x2 = 12 + -51x + 11x2 + -12 + 51x + -11x2 Reorder the terms: -380 + -56x + 4x2 = 12 + -12 + -51x + 51x + 11x2 + -11x2 Combine like terms: 12 + -12 = 0 -380 + -56x + 4x2 = 0 + -51x + 51x + 11x2 + -11x2 -380 + -56x + 4x2 = -51x + 51x + 11x2 + -11x2 Combine like terms: -51x + 51x = 0 -380 + -56x + 4x2 = 0 + 11x2 + -11x2 -380 + -56x + 4x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 -380 + -56x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-95 + -14x + x2) = 0 Factor a trinomial. 4((-5 + -1x)(19 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve: Simplifying 19 + -1x = 0 Solving 19 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1x = 0 + -19 -1x = 0 + -19 Combine like terms: 0 + -19 = -19 -1x = -19 Divide each side by '-1'. x = 19 Simplifying x = 19Solution
x = {-5, 19}
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