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Simplifying 0 = -7w3 + 28w2 + -21w Reorder the terms: 0 = -21w + 28w2 + -7w3 Solving 0 = -21w + 28w2 + -7w3 Solving for variable 'w'. Remove the zero: 21w + -28w2 + 7w3 = -21w + 28w2 + -7w3 + 21w + -28w2 + 7w3 Reorder the terms: 21w + -28w2 + 7w3 = -21w + 21w + 28w2 + -28w2 + -7w3 + 7w3 Combine like terms: -21w + 21w = 0 21w + -28w2 + 7w3 = 0 + 28w2 + -28w2 + -7w3 + 7w3 21w + -28w2 + 7w3 = 28w2 + -28w2 + -7w3 + 7w3 Combine like terms: 28w2 + -28w2 = 0 21w + -28w2 + 7w3 = 0 + -7w3 + 7w3 21w + -28w2 + 7w3 = -7w3 + 7w3 Combine like terms: -7w3 + 7w3 = 0 21w + -28w2 + 7w3 = 0 Factor out the Greatest Common Factor (GCF), '7w'. 7w(3 + -4w + w2) = 0 Factor a trinomial. 7w((1 + -1w)(3 + -1w)) = 0 Ignore the factor 7.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 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 3
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {0, 1, 3}
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