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Simplifying (1 + w)(5w + 7) = 0 Reorder the terms: (1 + w)(7 + 5w) = 0 Multiply (1 + w) * (7 + 5w) (1(7 + 5w) + w(7 + 5w)) = 0 ((7 * 1 + 5w * 1) + w(7 + 5w)) = 0 ((7 + 5w) + w(7 + 5w)) = 0 (7 + 5w + (7 * w + 5w * w)) = 0 (7 + 5w + (7w + 5w2)) = 0 Combine like terms: 5w + 7w = 12w (7 + 12w + 5w2) = 0 Solving 7 + 12w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + 5w)(1 + w) = 0Subproblem 1
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 = -1.4Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {-1.4, -1}
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