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Simplifying 10w3 + -40w2 + 14w2 + -56w = 0 Reorder the terms: -56w + -40w2 + 14w2 + 10w3 = 0 Combine like terms: -40w2 + 14w2 = -26w2 -56w + -26w2 + 10w3 = 0 Solving -56w + -26w2 + 10w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(-28 + -13w + 5w2) = 0 Factor a trinomial. 2w((-7 + -5w)(4 + -1w)) = 0 Ignore the factor 2.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 '(-7 + -5w)' equal to zero and attempt to solve: Simplifying -7 + -5w = 0 Solving -7 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5w = 0 + 7 -5w = 0 + 7 Combine like terms: 0 + 7 = 7 -5w = 7 Divide each side by '-5'. w = -1.4 Simplifying w = -1.4Subproblem 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, -1.4, 4}
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