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Simplifying (2 + w)(5w + 7) = 0 Reorder the terms: (2 + w)(7 + 5w) = 0 Multiply (2 + w) * (7 + 5w) (2(7 + 5w) + w(7 + 5w)) = 0 ((7 * 2 + 5w * 2) + w(7 + 5w)) = 0 ((14 + 10w) + w(7 + 5w)) = 0 (14 + 10w + (7 * w + 5w * w)) = 0 (14 + 10w + (7w + 5w2)) = 0 Combine like terms: 10w + 7w = 17w (14 + 17w + 5w2) = 0 Solving 14 + 17w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (2 + w)(7 + 5w) = 0Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Subproblem 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 = {-2, -1.4}
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