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Simplifying 5w3 = 40w2 + -80w Reorder the terms: 5w3 = -80w + 40w2 Solving 5w3 = -80w + 40w2 Solving for variable 'w'. Reorder the terms: 80w + -40w2 + 5w3 = -80w + 40w2 + 80w + -40w2 Reorder the terms: 80w + -40w2 + 5w3 = -80w + 80w + 40w2 + -40w2 Combine like terms: -80w + 80w = 0 80w + -40w2 + 5w3 = 0 + 40w2 + -40w2 80w + -40w2 + 5w3 = 40w2 + -40w2 Combine like terms: 40w2 + -40w2 = 0 80w + -40w2 + 5w3 = 0 Factor out the Greatest Common Factor (GCF), '5w'. 5w(16 + -8w + w2) = 0 Factor a trinomial. 5w((4 + -1w)(4 + -1w)) = 0 Ignore the factor 5.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 '(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 = 4Subproblem 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, 4, 4}
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