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Simplifying 2w4 + -24w3 + 72w2 = 0 Reorder the terms: 72w2 + -24w3 + 2w4 = 0 Solving 72w2 + -24w3 + 2w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w2'. 2w2(36 + -12w + w2) = 0 Factor a trinomial. 2w2((6 + -1w)(6 + -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 '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 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 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Subproblem 3
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 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 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {0, 6, 6}
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