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Simplifying 20w3 + -45w = 0 Reorder the terms: -45w + 20w3 = 0 Solving -45w + 20w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(-9 + 4w2) = 0 Factor a difference between two squares. 5w((3 + 2w)(-3 + 2w)) = 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 '(3 + 2w)' equal to zero and attempt to solve: Simplifying 3 + 2w = 0 Solving 3 + 2w = 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 + 2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2w = 0 + -3 2w = 0 + -3 Combine like terms: 0 + -3 = -3 2w = -3 Divide each side by '2'. w = -1.5 Simplifying w = -1.5Subproblem 3
Set the factor '(-3 + 2w)' equal to zero and attempt to solve: Simplifying -3 + 2w = 0 Solving -3 + 2w = 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 + 2w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2w = 0 + 3 2w = 0 + 3 Combine like terms: 0 + 3 = 3 2w = 3 Divide each side by '2'. w = 1.5 Simplifying w = 1.5Solution
w = {0, -1.5, 1.5}
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