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Simplifying (4w + 5)(7 + w) = 0 Reorder the terms: (5 + 4w)(7 + w) = 0 Multiply (5 + 4w) * (7 + w) (5(7 + w) + 4w * (7 + w)) = 0 ((7 * 5 + w * 5) + 4w * (7 + w)) = 0 ((35 + 5w) + 4w * (7 + w)) = 0 (35 + 5w + (7 * 4w + w * 4w)) = 0 (35 + 5w + (28w + 4w2)) = 0 Combine like terms: 5w + 28w = 33w (35 + 33w + 4w2) = 0 Solving 35 + 33w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + w)(5 + 4w) = 0Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Subproblem 2
Set the factor '(5 + 4w)' equal to zero and attempt to solve: Simplifying 5 + 4w = 0 Solving 5 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4w = 0 + -5 4w = 0 + -5 Combine like terms: 0 + -5 = -5 4w = -5 Divide each side by '4'. w = -1.25 Simplifying w = -1.25Solution
w = {-7, -1.25}
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