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Simplifying 8w3 + -30w2 + -8w = 0 Reorder the terms: -8w + -30w2 + 8w3 = 0 Solving -8w + -30w2 + 8w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(-4 + -15w + 4w2) = 0 Factor a trinomial. 2w((-1 + -4w)(4 + -1w)) = 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 '(-1 + -4w)' equal to zero and attempt to solve: Simplifying -1 + -4w = 0 Solving -1 + -4w = 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 + -4w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4w = 0 + 1 -4w = 0 + 1 Combine like terms: 0 + 1 = 1 -4w = 1 Divide each side by '-4'. w = -0.25 Simplifying w = -0.25Subproblem 3
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {0, -0.25, 4}
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