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Simplifying (12 + 2X)(16 + 2X) = 0 Multiply (12 + 2X) * (16 + 2X) (12(16 + 2X) + 2X * (16 + 2X)) = 0 ((16 * 12 + 2X * 12) + 2X * (16 + 2X)) = 0 ((192 + 24X) + 2X * (16 + 2X)) = 0 (192 + 24X + (16 * 2X + 2X * 2X)) = 0 (192 + 24X + (32X + 4X2)) = 0 Combine like terms: 24X + 32X = 56X (192 + 56X + 4X2) = 0 Solving 192 + 56X + 4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(48 + 14X + X2) = 0 Factor a trinomial. 4((8 + X)(6 + X)) = 0 Ignore the factor 4.Subproblem 1
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 = -8Subproblem 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 = {-8, -6}
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