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Simplifying (w + 5) = 2w2 + 17w + 35 Reorder the terms: (5 + w) = 2w2 + 17w + 35 Remove parenthesis around (5 + w) 5 + w = 2w2 + 17w + 35 Reorder the terms: 5 + w = 35 + 17w + 2w2 Solving 5 + w = 35 + 17w + 2w2 Solving for variable 'w'. Reorder the terms: 5 + -35 + w + -17w + -2w2 = 35 + 17w + 2w2 + -35 + -17w + -2w2 Combine like terms: 5 + -35 = -30 -30 + w + -17w + -2w2 = 35 + 17w + 2w2 + -35 + -17w + -2w2 Combine like terms: w + -17w = -16w -30 + -16w + -2w2 = 35 + 17w + 2w2 + -35 + -17w + -2w2 Reorder the terms: -30 + -16w + -2w2 = 35 + -35 + 17w + -17w + 2w2 + -2w2 Combine like terms: 35 + -35 = 0 -30 + -16w + -2w2 = 0 + 17w + -17w + 2w2 + -2w2 -30 + -16w + -2w2 = 17w + -17w + 2w2 + -2w2 Combine like terms: 17w + -17w = 0 -30 + -16w + -2w2 = 0 + 2w2 + -2w2 -30 + -16w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -30 + -16w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(15 + 8w + w2) = 0 Factor a trinomial. -2((5 + w)(3 + w)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {-5, -3}
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