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Simplifying (6x + 12)(9x + 18) = 0 Reorder the terms: (12 + 6x)(9x + 18) = 0 Reorder the terms: (12 + 6x)(18 + 9x) = 0 Multiply (12 + 6x) * (18 + 9x) (12(18 + 9x) + 6x * (18 + 9x)) = 0 ((18 * 12 + 9x * 12) + 6x * (18 + 9x)) = 0 ((216 + 108x) + 6x * (18 + 9x)) = 0 (216 + 108x + (18 * 6x + 9x * 6x)) = 0 (216 + 108x + (108x + 54x2)) = 0 Combine like terms: 108x + 108x = 216x (216 + 216x + 54x2) = 0 Solving 216 + 216x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '54'. 54(4 + 4x + x2) = 0 Factor a trinomial. 54((2 + x)(2 + x)) = 0 Ignore the factor 54.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2, -2}
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