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Simplifying 5w(7w + -5)(5w + -1) = 0 Reorder the terms: 5w(-5 + 7w)(5w + -1) = 0 Reorder the terms: 5w(-5 + 7w)(-1 + 5w) = 0 Multiply (-5 + 7w) * (-1 + 5w) 5w(-5(-1 + 5w) + 7w * (-1 + 5w)) = 0 5w((-1 * -5 + 5w * -5) + 7w * (-1 + 5w)) = 0 5w((5 + -25w) + 7w * (-1 + 5w)) = 0 5w(5 + -25w + (-1 * 7w + 5w * 7w)) = 0 5w(5 + -25w + (-7w + 35w2)) = 0 Combine like terms: -25w + -7w = -32w 5w(5 + -32w + 35w2) = 0 (5 * 5w + -32w * 5w + 35w2 * 5w) = 0 (25w + -160w2 + 175w3) = 0 Solving 25w + -160w2 + 175w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(5 + -32w + 35w2) = 0 Factor a trinomial. 5w((1 + -5w)(5 + -7w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(1 + -5w)' equal to zero and attempt to solve: Simplifying 1 + -5w = 0 Solving 1 + -5w = 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 + -5w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5w = 0 + -1 -5w = 0 + -1 Combine like terms: 0 + -1 = -1 -5w = -1 Divide each side by '-5'. w = 0.2 Simplifying w = 0.2Subproblem 3
Set the factor '(5 + -7w)' equal to zero and attempt to solve: Simplifying 5 + -7w = 0 Solving 5 + -7w = 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 + -7w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7w = 0 + -5 -7w = 0 + -5 Combine like terms: 0 + -5 = -5 -7w = -5 Divide each side by '-7'. w = 0.7142857143 Simplifying w = 0.7142857143Solution
w = {0, 0.2, 0.7142857143}
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