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Simplifying (3 + w)(2w + 9) = 0 Reorder the terms: (3 + w)(9 + 2w) = 0 Multiply (3 + w) * (9 + 2w) (3(9 + 2w) + w(9 + 2w)) = 0 ((9 * 3 + 2w * 3) + w(9 + 2w)) = 0 ((27 + 6w) + w(9 + 2w)) = 0 (27 + 6w + (9 * w + 2w * w)) = 0 (27 + 6w + (9w + 2w2)) = 0 Combine like terms: 6w + 9w = 15w (27 + 15w + 2w2) = 0 Solving 27 + 15w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + 2w)(3 + w) = 0Subproblem 1
Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 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 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 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 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {-4.5, -3}
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