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Simplifying (4 + w)(2w + 7) = 0 Reorder the terms: (4 + w)(7 + 2w) = 0 Multiply (4 + w) * (7 + 2w) (4(7 + 2w) + w(7 + 2w)) = 0 ((7 * 4 + 2w * 4) + w(7 + 2w)) = 0 ((28 + 8w) + w(7 + 2w)) = 0 (28 + 8w + (7 * w + 2w * w)) = 0 (28 + 8w + (7w + 2w2)) = 0 Combine like terms: 8w + 7w = 15w (28 + 15w + 2w2) = 0 Solving 28 + 15w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + w)(7 + 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 '(7 + 2w)' equal to zero and attempt to solve: Simplifying 7 + 2w = 0 Solving 7 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2w = 0 + -7 2w = 0 + -7 Combine like terms: 0 + -7 = -7 2w = -7 Divide each side by '2'. w = -3.5 Simplifying w = -3.5Solution
w = {-4, -3.5}
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