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Simplifying 5w9 + -16w8 + -35w7 = 9w8 + -5w7 Reorder the terms: -35w7 + -16w8 + 5w9 = 9w8 + -5w7 Reorder the terms: -35w7 + -16w8 + 5w9 = -5w7 + 9w8 Solving -35w7 + -16w8 + 5w9 = -5w7 + 9w8 Solving for variable 'w'. Reorder the terms: -35w7 + 5w7 + -16w8 + -9w8 + 5w9 = -5w7 + 9w8 + 5w7 + -9w8 Combine like terms: -35w7 + 5w7 = -30w7 -30w7 + -16w8 + -9w8 + 5w9 = -5w7 + 9w8 + 5w7 + -9w8 Combine like terms: -16w8 + -9w8 = -25w8 -30w7 + -25w8 + 5w9 = -5w7 + 9w8 + 5w7 + -9w8 Reorder the terms: -30w7 + -25w8 + 5w9 = -5w7 + 5w7 + 9w8 + -9w8 Combine like terms: -5w7 + 5w7 = 0 -30w7 + -25w8 + 5w9 = 0 + 9w8 + -9w8 -30w7 + -25w8 + 5w9 = 9w8 + -9w8 Combine like terms: 9w8 + -9w8 = 0 -30w7 + -25w8 + 5w9 = 0 Factor out the Greatest Common Factor (GCF), '5w7'. 5w7(-6 + -5w + w2) = 0 Factor a trinomial. 5w7((-1 + -1w)(6 + -1w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'w7' equal to zero and attempt to solve: Simplifying w7 = 0 Solving w7 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w7 = 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 '(-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 '(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 = {-1, 6}
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