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Simplifying w(w + 3) + 66 = 2(2w + 6)(w + -1) Reorder the terms: w(3 + w) + 66 = 2(2w + 6)(w + -1) (3 * w + w * w) + 66 = 2(2w + 6)(w + -1) (3w + w2) + 66 = 2(2w + 6)(w + -1) Reorder the terms: 66 + 3w + w2 = 2(2w + 6)(w + -1) Reorder the terms: 66 + 3w + w2 = 2(6 + 2w)(w + -1) Reorder the terms: 66 + 3w + w2 = 2(6 + 2w)(-1 + w) Multiply (6 + 2w) * (-1 + w) 66 + 3w + w2 = 2(6(-1 + w) + 2w * (-1 + w)) 66 + 3w + w2 = 2((-1 * 6 + w * 6) + 2w * (-1 + w)) 66 + 3w + w2 = 2((-6 + 6w) + 2w * (-1 + w)) 66 + 3w + w2 = 2(-6 + 6w + (-1 * 2w + w * 2w)) 66 + 3w + w2 = 2(-6 + 6w + (-2w + 2w2)) Combine like terms: 6w + -2w = 4w 66 + 3w + w2 = 2(-6 + 4w + 2w2) 66 + 3w + w2 = (-6 * 2 + 4w * 2 + 2w2 * 2) 66 + 3w + w2 = (-12 + 8w + 4w2) Solving 66 + 3w + w2 = -12 + 8w + 4w2 Solving for variable 'w'. Reorder the terms: 66 + 12 + 3w + -8w + w2 + -4w2 = -12 + 8w + 4w2 + 12 + -8w + -4w2 Combine like terms: 66 + 12 = 78 78 + 3w + -8w + w2 + -4w2 = -12 + 8w + 4w2 + 12 + -8w + -4w2 Combine like terms: 3w + -8w = -5w 78 + -5w + w2 + -4w2 = -12 + 8w + 4w2 + 12 + -8w + -4w2 Combine like terms: w2 + -4w2 = -3w2 78 + -5w + -3w2 = -12 + 8w + 4w2 + 12 + -8w + -4w2 Reorder the terms: 78 + -5w + -3w2 = -12 + 12 + 8w + -8w + 4w2 + -4w2 Combine like terms: -12 + 12 = 0 78 + -5w + -3w2 = 0 + 8w + -8w + 4w2 + -4w2 78 + -5w + -3w2 = 8w + -8w + 4w2 + -4w2 Combine like terms: 8w + -8w = 0 78 + -5w + -3w2 = 0 + 4w2 + -4w2 78 + -5w + -3w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 78 + -5w + -3w2 = 0 Factor a trinomial. (13 + -3w)(6 + w) = 0Subproblem 1
Set the factor '(13 + -3w)' equal to zero and attempt to solve: Simplifying 13 + -3w = 0 Solving 13 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3w = 0 + -13 -3w = 0 + -13 Combine like terms: 0 + -13 = -13 -3w = -13 Divide each side by '-3'. w = 4.333333333 Simplifying w = 4.333333333Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 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 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Solution
w = {4.333333333, -6}
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