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Simplifying 12X = 3X2 + -96 Reorder the terms: 12X = -96 + 3X2 Solving 12X = -96 + 3X2 Solving for variable 'X'. Reorder the terms: 96 + 12X + -3X2 = -96 + 3X2 + 96 + -3X2 Reorder the terms: 96 + 12X + -3X2 = -96 + 96 + 3X2 + -3X2 Combine like terms: -96 + 96 = 0 96 + 12X + -3X2 = 0 + 3X2 + -3X2 96 + 12X + -3X2 = 3X2 + -3X2 Combine like terms: 3X2 + -3X2 = 0 96 + 12X + -3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(32 + 4X + -1X2) = 0 Factor a trinomial. 3((8 + -1X)(4 + X)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -1X)' equal to zero and attempt to solve: Simplifying 8 + -1X = 0 Solving 8 + -1X = 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 + -1X = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1X = 0 + -8 -1X = 0 + -8 Combine like terms: 0 + -8 = -8 -1X = -8 Divide each side by '-1'. X = 8 Simplifying X = 8Subproblem 2
Set the factor '(4 + X)' equal to zero and attempt to solve: Simplifying 4 + X = 0 Solving 4 + X = 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 + X = 0 + -4 Combine like terms: 4 + -4 = 0 0 + X = 0 + -4 X = 0 + -4 Combine like terms: 0 + -4 = -4 X = -4 Simplifying X = -4Solution
X = {8, -4}
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