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Simplifying (w + 5)(w + -7) = 0 Reorder the terms: (5 + w)(w + -7) = 0 Reorder the terms: (5 + w)(-7 + w) = 0 Multiply (5 + w) * (-7 + w) (5(-7 + w) + w(-7 + w)) = 0 ((-7 * 5 + w * 5) + w(-7 + w)) = 0 ((-35 + 5w) + w(-7 + w)) = 0 (-35 + 5w + (-7 * w + w * w)) = 0 (-35 + 5w + (-7w + w2)) = 0 Combine like terms: 5w + -7w = -2w (-35 + -2w + w2) = 0 Solving -35 + -2w + w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(7 + -1w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 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 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-5, 7}
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