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Simplifying 112w3 + 34w2 + -6w = 0 Reorder the terms: -6w + 34w2 + 112w3 = 0 Solving -6w + 34w2 + 112w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(-3 + 17w + 56w2) = 0 Factor a trinomial. 2w((-3 + -7w)(1 + -8w)) = 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 '(-3 + -7w)' equal to zero and attempt to solve: Simplifying -3 + -7w = 0 Solving -3 + -7w = 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 + -7w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7w = 0 + 3 -7w = 0 + 3 Combine like terms: 0 + 3 = 3 -7w = 3 Divide each side by '-7'. w = -0.4285714286 Simplifying w = -0.4285714286Subproblem 3
Set the factor '(1 + -8w)' equal to zero and attempt to solve: Simplifying 1 + -8w = 0 Solving 1 + -8w = 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 + -8w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8w = 0 + -1 -8w = 0 + -1 Combine like terms: 0 + -1 = -1 -8w = -1 Divide each side by '-8'. w = 0.125 Simplifying w = 0.125Solution
w = {0, -0.4285714286, 0.125}
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