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Simplifying 2w7 + -34w6 + -76w5 = 0 Reorder the terms: -76w5 + -34w6 + 2w7 = 0 Solving -76w5 + -34w6 + 2w7 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w5'. 2w5(-38 + -17w + w2) = 0 Factor a trinomial. 2w5((-2 + -1w)(19 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'w5' equal to zero and attempt to solve: Simplifying w5 = 0 Solving w5 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
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 = -2Subproblem 3
Set the factor '(19 + -1w)' equal to zero and attempt to solve: Simplifying 19 + -1w = 0 Solving 19 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1w = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1w = 0 + -19 -1w = 0 + -19 Combine like terms: 0 + -19 = -19 -1w = -19 Divide each side by '-1'. w = 19 Simplifying w = 19Solution
w = {-2, 19}
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