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Simplifying 14w3 + -23w2 + 8w = 0 Reorder the terms: 8w + -23w2 + 14w3 = 0 Solving 8w + -23w2 + 14w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(8 + -23w + 14w2) = 0 Factor a trinomial. w((1 + -2w)(8 + -7w)) = 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 '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 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 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Subproblem 3
Set the factor '(8 + -7w)' equal to zero and attempt to solve: Simplifying 8 + -7w = 0 Solving 8 + -7w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7w = 0 + -8 -7w = 0 + -8 Combine like terms: 0 + -8 = -8 -7w = -8 Divide each side by '-7'. w = 1.142857143 Simplifying w = 1.142857143Solution
w = {0, 0.5, 1.142857143}
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