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Simplifying 7w7 + -8w6 + -63w5 = 6w6 + -7w5 Reorder the terms: -63w5 + -8w6 + 7w7 = 6w6 + -7w5 Reorder the terms: -63w5 + -8w6 + 7w7 = -7w5 + 6w6 Solving -63w5 + -8w6 + 7w7 = -7w5 + 6w6 Solving for variable 'w'. Reorder the terms: -63w5 + 7w5 + -8w6 + -6w6 + 7w7 = -7w5 + 6w6 + 7w5 + -6w6 Combine like terms: -63w5 + 7w5 = -56w5 -56w5 + -8w6 + -6w6 + 7w7 = -7w5 + 6w6 + 7w5 + -6w6 Combine like terms: -8w6 + -6w6 = -14w6 -56w5 + -14w6 + 7w7 = -7w5 + 6w6 + 7w5 + -6w6 Reorder the terms: -56w5 + -14w6 + 7w7 = -7w5 + 7w5 + 6w6 + -6w6 Combine like terms: -7w5 + 7w5 = 0 -56w5 + -14w6 + 7w7 = 0 + 6w6 + -6w6 -56w5 + -14w6 + 7w7 = 6w6 + -6w6 Combine like terms: 6w6 + -6w6 = 0 -56w5 + -14w6 + 7w7 = 0 Factor out the Greatest Common Factor (GCF), '7w5'. 7w5(-8 + -2w + w2) = 0 Factor a trinomial. 7w5((-2 + -1w)(4 + -1w)) = 0 Ignore the factor 7.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 '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-2, 4}
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