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Simplifying (3 + w)(5w + -7) = 0 Reorder the terms: (3 + w)(-7 + 5w) = 0 Multiply (3 + w) * (-7 + 5w) (3(-7 + 5w) + w(-7 + 5w)) = 0 ((-7 * 3 + 5w * 3) + w(-7 + 5w)) = 0 ((-21 + 15w) + w(-7 + 5w)) = 0 (-21 + 15w + (-7 * w + 5w * w)) = 0 (-21 + 15w + (-7w + 5w2)) = 0 Combine like terms: 15w + -7w = 8w (-21 + 8w + 5w2) = 0 Solving -21 + 8w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + -1w)(7 + -5w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. 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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