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Simplifying 32w3 + -8w2 + -4w = 0 Reorder the terms: -4w + -8w2 + 32w3 = 0 Solving -4w + -8w2 + 32w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4w'. 4w(-1 + -2w + 8w2) = 0 Factor a trinomial. 4w((-1 + -4w)(1 + -2w)) = 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 '(-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 '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 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 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Solution
w = {0, -0.25, 0.5}
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