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Simplifying 96 = (12 + 2x)(8 + 2x) Multiply (12 + 2x) * (8 + 2x) 96 = (12(8 + 2x) + 2x * (8 + 2x)) 96 = ((8 * 12 + 2x * 12) + 2x * (8 + 2x)) 96 = ((96 + 24x) + 2x * (8 + 2x)) 96 = (96 + 24x + (8 * 2x + 2x * 2x)) 96 = (96 + 24x + (16x + 4x2)) Combine like terms: 24x + 16x = 40x 96 = (96 + 40x + 4x2) Add '-96' to each side of the equation. 96 + -96 = 96 + 40x + -96 + 4x2 Combine like terms: 96 + -96 = 0 0 = 96 + 40x + -96 + 4x2 Reorder the terms: 0 = 96 + -96 + 40x + 4x2 Combine like terms: 96 + -96 = 0 0 = 0 + 40x + 4x2 0 = 40x + 4x2 Solving 0 = 40x + 4x2 Solving for variable 'x'. Remove the zero: -40x + -4x2 = 40x + 4x2 + -40x + -4x2 Reorder the terms: -40x + -4x2 = 40x + -40x + 4x2 + -4x2 Combine like terms: 40x + -40x = 0 -40x + -4x2 = 0 + 4x2 + -4x2 -40x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -40x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4x'. -4x(10 + x) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {0, -10}
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