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Simplifying -10w3 + 30w2 + -4w2 + 12w = 0 Reorder the terms: 12w + 30w2 + -4w2 + -10w3 = 0 Combine like terms: 30w2 + -4w2 = 26w2 12w + 26w2 + -10w3 = 0 Solving 12w + 26w2 + -10w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(6 + 13w + -5w2) = 0 Factor a trinomial. 2w((3 + -1w)(2 + 5w)) = 0 Ignore the factor 2.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 + -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 3
Set the factor '(2 + 5w)' equal to zero and attempt to solve: Simplifying 2 + 5w = 0 Solving 2 + 5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5w = 0 + -2 5w = 0 + -2 Combine like terms: 0 + -2 = -2 5w = -2 Divide each side by '5'. w = -0.4 Simplifying w = -0.4Solution
w = {0, 3, -0.4}
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