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Simplifying 6w4 + -2w3 + -20w2 = 0 Reorder the terms: -20w2 + -2w3 + 6w4 = 0 Solving -20w2 + -2w3 + 6w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w2'. 2w2(-10 + -1w + 3w2) = 0 Factor a trinomial. 2w2((-5 + -3w)(2 + -1w)) = 0 Ignore the factor 2.Subproblem 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 '(-5 + -3w)' equal to zero and attempt to solve: Simplifying -5 + -3w = 0 Solving -5 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3w = 0 + 5 -3w = 0 + 5 Combine like terms: 0 + 5 = 5 -3w = 5 Divide each side by '-3'. w = -1.666666667 Simplifying w = -1.666666667Subproblem 3
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 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 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {0, -1.666666667, 2}
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