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Simplifying 0 = 28w3 + 84w2 + 20w2 + 60w Reorder the terms: 0 = 60w + 84w2 + 20w2 + 28w3 Combine like terms: 84w2 + 20w2 = 104w2 0 = 60w + 104w2 + 28w3 Solving 0 = 60w + 104w2 + 28w3 Solving for variable 'w'. Remove the zero: -60w + -104w2 + -28w3 = 60w + 104w2 + 28w3 + -60w + -104w2 + -28w3 Reorder the terms: -60w + -104w2 + -28w3 = 60w + -60w + 104w2 + -104w2 + 28w3 + -28w3 Combine like terms: 60w + -60w = 0 -60w + -104w2 + -28w3 = 0 + 104w2 + -104w2 + 28w3 + -28w3 -60w + -104w2 + -28w3 = 104w2 + -104w2 + 28w3 + -28w3 Combine like terms: 104w2 + -104w2 = 0 -60w + -104w2 + -28w3 = 0 + 28w3 + -28w3 -60w + -104w2 + -28w3 = 28w3 + -28w3 Combine like terms: 28w3 + -28w3 = 0 -60w + -104w2 + -28w3 = 0 Factor out the Greatest Common Factor (GCF), '-4w'. -4w(15 + 26w + 7w2) = 0 Factor a trinomial. -4w((3 + w)(5 + 7w)) = 0 Ignore the factor -4.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 '(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 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, -3, -0.7142857143}
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