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Simplifying (w + 7)(w + 5) = 0 Reorder the terms: (7 + w)(w + 5) = 0 Reorder the terms: (7 + w)(5 + w) = 0 Multiply (7 + w) * (5 + w) (7(5 + w) + w(5 + w)) = 0 ((5 * 7 + w * 7) + w(5 + w)) = 0 ((35 + 7w) + w(5 + w)) = 0 (35 + 7w + (5 * w + w * w)) = 0 (35 + 7w + (5w + w2)) = 0 Combine like terms: 7w + 5w = 12w (35 + 12w + w2) = 0 Solving 35 + 12w + w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + w)(5 + w) = 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 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Solution
w = {-7, -5}
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