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Simplifying w3 + -1w(w2 + 2w + -1) + 2w = 0 Reorder the terms: w3 + -1w(-1 + 2w + w2) + 2w = 0 w3 + (-1 * -1w + 2w * -1w + w2 * -1w) + 2w = 0 w3 + (1w + -2w2 + -1w3) + 2w = 0 Reorder the terms: 1w + 2w + -2w2 + w3 + -1w3 = 0 Combine like terms: 1w + 2w = 3w 3w + -2w2 + w3 + -1w3 = 0 Combine like terms: w3 + -1w3 = 0 3w + -2w2 + 0 = 0 3w + -2w2 = 0 Solving 3w + -2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(3 + -2w) = 0Subproblem 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 = 1.5Solution
w = {0, 1.5}
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