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Simplifying 8w3 + 14w2 + 3w = 0 Reorder the terms: 3w + 14w2 + 8w3 = 0 Solving 3w + 14w2 + 8w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(3 + 14w + 8w2) = 0 Factor a trinomial. w((3 + 2w)(1 + 4w)) = 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 '(3 + 2w)' equal to zero and attempt to solve: Simplifying 3 + 2w = 0 Solving 3 + 2w = 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 + 2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2w = 0 + -3 2w = 0 + -3 Combine like terms: 0 + -3 = -3 2w = -3 Divide each side by '2'. w = -1.5 Simplifying w = -1.5Subproblem 3
Set the factor '(1 + 4w)' equal to zero and attempt to solve: Simplifying 1 + 4w = 0 Solving 1 + 4w = 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 + 4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4w = 0 + -1 4w = 0 + -1 Combine like terms: 0 + -1 = -1 4w = -1 Divide each side by '4'. w = -0.25 Simplifying w = -0.25Solution
w = {0, -1.5, -0.25}
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