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Simplifying 18w3 + -33w2 + 14w = 0 Reorder the terms: 14w + -33w2 + 18w3 = 0 Solving 14w + -33w2 + 18w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(14 + -33w + 18w2) = 0 Factor a trinomial. w((2 + -3w)(7 + -6w)) = 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 '(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 = 0.6666666667Subproblem 3
Set the factor '(7 + -6w)' equal to zero and attempt to solve: Simplifying 7 + -6w = 0 Solving 7 + -6w = 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 + -6w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6w = 0 + -7 -6w = 0 + -7 Combine like terms: 0 + -7 = -7 -6w = -7 Divide each side by '-6'. w = 1.166666667 Simplifying w = 1.166666667Solution
w = {0, 0.6666666667, 1.166666667}
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