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Simplifying (2w + -12)(w + 9) = 0 Reorder the terms: (-12 + 2w)(w + 9) = 0 Reorder the terms: (-12 + 2w)(9 + w) = 0 Multiply (-12 + 2w) * (9 + w) (-12(9 + w) + 2w * (9 + w)) = 0 ((9 * -12 + w * -12) + 2w * (9 + w)) = 0 ((-108 + -12w) + 2w * (9 + w)) = 0 (-108 + -12w + (9 * 2w + w * 2w)) = 0 (-108 + -12w + (18w + 2w2)) = 0 Combine like terms: -12w + 18w = 6w (-108 + 6w + 2w2) = 0 Solving -108 + 6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 3w + w2) = 0 Factor a trinomial. 2((-9 + -1w)(6 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {-9, 6}
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