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Simplifying 3x2 + -5x + -10 = x2 + 3x + 14 Reorder the terms: -10 + -5x + 3x2 = x2 + 3x + 14 Reorder the terms: -10 + -5x + 3x2 = 14 + 3x + x2 Solving -10 + -5x + 3x2 = 14 + 3x + x2 Solving for variable 'x'. Reorder the terms: -10 + -14 + -5x + -3x + 3x2 + -1x2 = 14 + 3x + x2 + -14 + -3x + -1x2 Combine like terms: -10 + -14 = -24 -24 + -5x + -3x + 3x2 + -1x2 = 14 + 3x + x2 + -14 + -3x + -1x2 Combine like terms: -5x + -3x = -8x -24 + -8x + 3x2 + -1x2 = 14 + 3x + x2 + -14 + -3x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -24 + -8x + 2x2 = 14 + 3x + x2 + -14 + -3x + -1x2 Reorder the terms: -24 + -8x + 2x2 = 14 + -14 + 3x + -3x + x2 + -1x2 Combine like terms: 14 + -14 = 0 -24 + -8x + 2x2 = 0 + 3x + -3x + x2 + -1x2 -24 + -8x + 2x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -24 + -8x + 2x2 = 0 + x2 + -1x2 -24 + -8x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -24 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -4x + x2) = 0 Factor a trinomial. 2((-2 + -1x)(6 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-2, 6}
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