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Simplifying 0 = 9w2 + 6w + -27w3 Reorder the terms: 0 = 6w + 9w2 + -27w3 Solving 0 = 6w + 9w2 + -27w3 Solving for variable 'w'. Remove the zero: -6w + -9w2 + 27w3 = 6w + 9w2 + -27w3 + -6w + -9w2 + 27w3 Reorder the terms: -6w + -9w2 + 27w3 = 6w + -6w + 9w2 + -9w2 + -27w3 + 27w3 Combine like terms: 6w + -6w = 0 -6w + -9w2 + 27w3 = 0 + 9w2 + -9w2 + -27w3 + 27w3 -6w + -9w2 + 27w3 = 9w2 + -9w2 + -27w3 + 27w3 Combine like terms: 9w2 + -9w2 = 0 -6w + -9w2 + 27w3 = 0 + -27w3 + 27w3 -6w + -9w2 + 27w3 = -27w3 + 27w3 Combine like terms: -27w3 + 27w3 = 0 -6w + -9w2 + 27w3 = 0 Factor out the Greatest Common Factor (GCF), '3w'. 3w(-2 + -3w + 9w2) = 0 Factor a trinomial. 3w((-1 + -3w)(2 + -3w)) = 0 Ignore the factor 3.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 '(-1 + -3w)' equal to zero and attempt to solve: Simplifying -1 + -3w = 0 Solving -1 + -3w = 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 + -3w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3w = 0 + 1 -3w = 0 + 1 Combine like terms: 0 + 1 = 1 -3w = 1 Divide each side by '-3'. w = -0.3333333333 Simplifying w = -0.3333333333Subproblem 3
Set the factor '(2 + -3w)' equal to zero and attempt to solve: Simplifying 2 + -3w = 0 Solving 2 + -3w = 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 + -3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3w = 0 + -2 -3w = 0 + -2 Combine like terms: 0 + -2 = -2 -3w = -2 Divide each side by '-3'. w = 0.6666666667 Simplifying w = 0.6666666667Solution
w = {0, -0.3333333333, 0.6666666667}
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