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Simplifying (24 + 2x)(12 + 2x) = 0 Multiply (24 + 2x) * (12 + 2x) (24(12 + 2x) + 2x * (12 + 2x)) = 0 ((12 * 24 + 2x * 24) + 2x * (12 + 2x)) = 0 ((288 + 48x) + 2x * (12 + 2x)) = 0 (288 + 48x + (12 * 2x + 2x * 2x)) = 0 (288 + 48x + (24x + 4x2)) = 0 Combine like terms: 48x + 24x = 72x (288 + 72x + 4x2) = 0 Solving 288 + 72x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(72 + 18x + x2) = 0 Factor a trinomial. 4((12 + x)(6 + x)) = 0 Ignore the factor 4.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 '(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 = {-12, -6}
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