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Simplifying 5w3 + 6w2 = 4w3 + -8w Reorder the terms: 6w2 + 5w3 = 4w3 + -8w Reorder the terms: 6w2 + 5w3 = -8w + 4w3 Solving 6w2 + 5w3 = -8w + 4w3 Solving for variable 'w'. Reorder the terms: 8w + 6w2 + 5w3 + -4w3 = -8w + 4w3 + 8w + -4w3 Combine like terms: 5w3 + -4w3 = 1w3 8w + 6w2 + 1w3 = -8w + 4w3 + 8w + -4w3 Reorder the terms: 8w + 6w2 + 1w3 = -8w + 8w + 4w3 + -4w3 Combine like terms: -8w + 8w = 0 8w + 6w2 + 1w3 = 0 + 4w3 + -4w3 8w + 6w2 + 1w3 = 4w3 + -4w3 Combine like terms: 4w3 + -4w3 = 0 8w + 6w2 + 1w3 = 0 Factor out the Greatest Common Factor (GCF), 'w'. w(8 + 6w + w2) = 0 Factor a trinomial. w((4 + w)(2 + w)) = 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 '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 3
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 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 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {0, -4, -2}
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