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Simplifying 4x2 + -108 = 5x2 + 21x Reorder the terms: -108 + 4x2 = 5x2 + 21x Reorder the terms: -108 + 4x2 = 21x + 5x2 Solving -108 + 4x2 = 21x + 5x2 Solving for variable 'x'. Reorder the terms: -108 + -21x + 4x2 + -5x2 = 21x + 5x2 + -21x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -108 + -21x + -1x2 = 21x + 5x2 + -21x + -5x2 Reorder the terms: -108 + -21x + -1x2 = 21x + -21x + 5x2 + -5x2 Combine like terms: 21x + -21x = 0 -108 + -21x + -1x2 = 0 + 5x2 + -5x2 -108 + -21x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -108 + -21x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(108 + 21x + x2) = 0 Factor a trinomial. -1((12 + x)(9 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Solution
x = {-12, -9}
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