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Simplifying (5w + -7)(3 + -1w) = 0 Reorder the terms: (-7 + 5w)(3 + -1w) = 0 Multiply (-7 + 5w) * (3 + -1w) (-7(3 + -1w) + 5w * (3 + -1w)) = 0 ((3 * -7 + -1w * -7) + 5w * (3 + -1w)) = 0 ((-21 + 7w) + 5w * (3 + -1w)) = 0 (-21 + 7w + (3 * 5w + -1w * 5w)) = 0 (-21 + 7w + (15w + -5w2)) = 0 Combine like terms: 7w + 15w = 22w (-21 + 22w + -5w2) = 0 Solving -21 + 22w + -5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + w)(7 + -5w) = 0Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve: Simplifying -3 + w = 0 Solving -3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w = 0 + 3 w = 0 + 3 Combine like terms: 0 + 3 = 3 w = 3 Simplifying w = 3Subproblem 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 = {3, 1.4}
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