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Simplifying (3w + 12)(w + 12) = 0 Reorder the terms: (12 + 3w)(w + 12) = 0 Reorder the terms: (12 + 3w)(12 + w) = 0 Multiply (12 + 3w) * (12 + w) (12(12 + w) + 3w * (12 + w)) = 0 ((12 * 12 + w * 12) + 3w * (12 + w)) = 0 ((144 + 12w) + 3w * (12 + w)) = 0 (144 + 12w + (12 * 3w + w * 3w)) = 0 (144 + 12w + (36w + 3w2)) = 0 Combine like terms: 12w + 36w = 48w (144 + 48w + 3w2) = 0 Solving 144 + 48w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(48 + 16w + w2) = 0 Factor a trinomial. 3((12 + w)(4 + w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + w)' equal to zero and attempt to solve: Simplifying 12 + w = 0 Solving 12 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + w = 0 + -12 w = 0 + -12 Combine like terms: 0 + -12 = -12 w = -12 Simplifying w = -12Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Solution
w = {-12, -4}
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