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Simplifying 20w4 + -39w3 + 18w2 = 0 Reorder the terms: 18w2 + -39w3 + 20w4 = 0 Solving 18w2 + -39w3 + 20w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w2'. w2(18 + -39w + 20w2) = 0 Factor a trinomial. w2((3 + -4w)(6 + -5w)) = 0Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w2 = 0 Take the square root of each side: w = {0}Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve: Simplifying 3 + -4w = 0 Solving 3 + -4w = 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 + -4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4w = 0 + -3 -4w = 0 + -3 Combine like terms: 0 + -3 = -3 -4w = -3 Divide each side by '-4'. w = 0.75 Simplifying w = 0.75Subproblem 3
Set the factor '(6 + -5w)' equal to zero and attempt to solve: Simplifying 6 + -5w = 0 Solving 6 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5w = 0 + -6 -5w = 0 + -6 Combine like terms: 0 + -6 = -6 -5w = -6 Divide each side by '-5'. w = 1.2 Simplifying w = 1.2Solution
w = {0, 0.75, 1.2}
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