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Simplifying (4 + w)(2w + 3) = 0 Reorder the terms: (4 + w)(3 + 2w) = 0 Multiply (4 + w) * (3 + 2w) (4(3 + 2w) + w(3 + 2w)) = 0 ((3 * 4 + 2w * 4) + w(3 + 2w)) = 0 ((12 + 8w) + w(3 + 2w)) = 0 (12 + 8w + (3 * w + 2w * w)) = 0 (12 + 8w + (3w + 2w2)) = 0 Combine like terms: 8w + 3w = 11w (12 + 11w + 2w2) = 0 Solving 12 + 11w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + w)(3 + 2w) = 0Subproblem 1
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 = -4Subproblem 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 = {-4, -1.5}
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