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Simplifying (4w + 6)(9 + w) = 0 Reorder the terms: (6 + 4w)(9 + w) = 0 Multiply (6 + 4w) * (9 + w) (6(9 + w) + 4w * (9 + w)) = 0 ((9 * 6 + w * 6) + 4w * (9 + w)) = 0 ((54 + 6w) + 4w * (9 + w)) = 0 (54 + 6w + (9 * 4w + w * 4w)) = 0 (54 + 6w + (36w + 4w2)) = 0 Combine like terms: 6w + 36w = 42w (54 + 42w + 4w2) = 0 Solving 54 + 42w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 21w + 2w2) = 0 Factor a trinomial. 2((9 + w)(3 + 2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve: Simplifying 9 + w = 0 Solving 9 + w = 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 + w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + w = 0 + -9 w = 0 + -9 Combine like terms: 0 + -9 = -9 w = -9 Simplifying w = -9Subproblem 2
Set the factor '(3 + 2w)' equal to zero and attempt to solve: Simplifying 3 + 2w = 0 Solving 3 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2w = 0 + -3 2w = 0 + -3 Combine like terms: 0 + -3 = -3 2w = -3 Divide each side by '2'. w = -1.5 Simplifying w = -1.5Solution
w = {-9, -1.5}
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