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Simplifying 4x2 + -96 = 5x2 + 20x Reorder the terms: -96 + 4x2 = 5x2 + 20x Reorder the terms: -96 + 4x2 = 20x + 5x2 Solving -96 + 4x2 = 20x + 5x2 Solving for variable 'x'. Reorder the terms: -96 + -20x + 4x2 + -5x2 = 20x + 5x2 + -20x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -96 + -20x + -1x2 = 20x + 5x2 + -20x + -5x2 Reorder the terms: -96 + -20x + -1x2 = 20x + -20x + 5x2 + -5x2 Combine like terms: 20x + -20x = 0 -96 + -20x + -1x2 = 0 + 5x2 + -5x2 -96 + -20x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -96 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(96 + 20x + x2) = 0 Factor a trinomial. -1((12 + x)(8 + 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {-12, -8}
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