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Simplifying (3x + 6)(x + 12) = 0 Reorder the terms: (6 + 3x)(x + 12) = 0 Reorder the terms: (6 + 3x)(12 + x) = 0 Multiply (6 + 3x) * (12 + x) (6(12 + x) + 3x * (12 + x)) = 0 ((12 * 6 + x * 6) + 3x * (12 + x)) = 0 ((72 + 6x) + 3x * (12 + x)) = 0 (72 + 6x + (12 * 3x + x * 3x)) = 0 (72 + 6x + (36x + 3x2)) = 0 Combine like terms: 6x + 36x = 42x (72 + 42x + 3x2) = 0 Solving 72 + 42x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(24 + 14x + x2) = 0 Factor a trinomial. 3((12 + x)(2 + x)) = 0 Ignore the factor 3.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 '(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 = {-12, -2}
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