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Simplifying (7w2 + 9w + 9) + -1(6w2 + -8w + -8) + (-3w2 + 5w + 7) = 0 Reorder the terms: (9 + 9w + 7w2) + -1(6w2 + -8w + -8) + (-3w2 + 5w + 7) = 0 Remove parenthesis around (9 + 9w + 7w2) 9 + 9w + 7w2 + -1(6w2 + -8w + -8) + (-3w2 + 5w + 7) = 0 Reorder the terms: 9 + 9w + 7w2 + -1(-8 + -8w + 6w2) + (-3w2 + 5w + 7) = 0 9 + 9w + 7w2 + (-8 * -1 + -8w * -1 + 6w2 * -1) + (-3w2 + 5w + 7) = 0 9 + 9w + 7w2 + (8 + 8w + -6w2) + (-3w2 + 5w + 7) = 0 Reorder the terms: 9 + 9w + 7w2 + 8 + 8w + -6w2 + (7 + 5w + -3w2) = 0 Remove parenthesis around (7 + 5w + -3w2) 9 + 9w + 7w2 + 8 + 8w + -6w2 + 7 + 5w + -3w2 = 0 Reorder the terms: 9 + 8 + 7 + 9w + 8w + 5w + 7w2 + -6w2 + -3w2 = 0 Combine like terms: 9 + 8 = 17 17 + 7 + 9w + 8w + 5w + 7w2 + -6w2 + -3w2 = 0 Combine like terms: 17 + 7 = 24 24 + 9w + 8w + 5w + 7w2 + -6w2 + -3w2 = 0 Combine like terms: 9w + 8w = 17w 24 + 17w + 5w + 7w2 + -6w2 + -3w2 = 0 Combine like terms: 17w + 5w = 22w 24 + 22w + 7w2 + -6w2 + -3w2 = 0 Combine like terms: 7w2 + -6w2 = 1w2 24 + 22w + 1w2 + -3w2 = 0 Combine like terms: 1w2 + -3w2 = -2w2 24 + 22w + -2w2 = 0 Solving 24 + 22w + -2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 11w + -1w2) = 0 Factor a trinomial. 2((12 + -1w)(1 + w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {12, -1}
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