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Simplifying 10w3 + 1w2 + -3w = 0 Reorder the terms: -3w + 1w2 + 10w3 = 0 Solving -3w + 1w2 + 10w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(-3 + w + 10w2) = 0 Factor a trinomial. w((-3 + -5w)(1 + -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 + -5w)' equal to zero and attempt to solve: Simplifying -3 + -5w = 0 Solving -3 + -5w = 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 + -5w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5w = 0 + 3 -5w = 0 + 3 Combine like terms: 0 + 3 = 3 -5w = 3 Divide each side by '-5'. w = -0.6 Simplifying w = -0.6Subproblem 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, -0.6, 0.5}
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