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Simplifying (5w + 7)(4 + w) = 0 Reorder the terms: (7 + 5w)(4 + w) = 0 Multiply (7 + 5w) * (4 + w) (7(4 + w) + 5w * (4 + w)) = 0 ((4 * 7 + w * 7) + 5w * (4 + w)) = 0 ((28 + 7w) + 5w * (4 + w)) = 0 (28 + 7w + (4 * 5w + w * 5w)) = 0 (28 + 7w + (20w + 5w2)) = 0 Combine like terms: 7w + 20w = 27w (28 + 27w + 5w2) = 0 Solving 28 + 27w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + w)(7 + 5w) = 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 + 5w)' equal to zero and attempt to solve: Simplifying 7 + 5w = 0 Solving 7 + 5w = 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 + 5w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5w = 0 + -7 5w = 0 + -7 Combine like terms: 0 + -7 = -7 5w = -7 Divide each side by '5'. w = -1.4 Simplifying w = -1.4Solution
w = {-4, -1.4}
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