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Simplifying (3w + 4)(9 + w) = 0 Reorder the terms: (4 + 3w)(9 + w) = 0 Multiply (4 + 3w) * (9 + w) (4(9 + w) + 3w * (9 + w)) = 0 ((9 * 4 + w * 4) + 3w * (9 + w)) = 0 ((36 + 4w) + 3w * (9 + w)) = 0 (36 + 4w + (9 * 3w + w * 3w)) = 0 (36 + 4w + (27w + 3w2)) = 0 Combine like terms: 4w + 27w = 31w (36 + 31w + 3w2) = 0 Solving 36 + 31w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + w)(4 + 3w) = 0Subproblem 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 '(4 + 3w)' equal to zero and attempt to solve: Simplifying 4 + 3w = 0 Solving 4 + 3w = 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 + 3w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3w = 0 + -4 3w = 0 + -4 Combine like terms: 0 + -4 = -4 3w = -4 Divide each side by '3'. w = -1.333333333 Simplifying w = -1.333333333Solution
w = {-9, -1.333333333}
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