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Simplifying 4x2 + -11x + 102 = 8x2 + -3x + 6 Reorder the terms: 102 + -11x + 4x2 = 8x2 + -3x + 6 Reorder the terms: 102 + -11x + 4x2 = 6 + -3x + 8x2 Solving 102 + -11x + 4x2 = 6 + -3x + 8x2 Solving for variable 'x'. Reorder the terms: 102 + -6 + -11x + 3x + 4x2 + -8x2 = 6 + -3x + 8x2 + -6 + 3x + -8x2 Combine like terms: 102 + -6 = 96 96 + -11x + 3x + 4x2 + -8x2 = 6 + -3x + 8x2 + -6 + 3x + -8x2 Combine like terms: -11x + 3x = -8x 96 + -8x + 4x2 + -8x2 = 6 + -3x + 8x2 + -6 + 3x + -8x2 Combine like terms: 4x2 + -8x2 = -4x2 96 + -8x + -4x2 = 6 + -3x + 8x2 + -6 + 3x + -8x2 Reorder the terms: 96 + -8x + -4x2 = 6 + -6 + -3x + 3x + 8x2 + -8x2 Combine like terms: 6 + -6 = 0 96 + -8x + -4x2 = 0 + -3x + 3x + 8x2 + -8x2 96 + -8x + -4x2 = -3x + 3x + 8x2 + -8x2 Combine like terms: -3x + 3x = 0 96 + -8x + -4x2 = 0 + 8x2 + -8x2 96 + -8x + -4x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 96 + -8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(24 + -2x + -1x2) = 0 Factor a trinomial. 4((4 + -1x)(6 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {4, -6}
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