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Simplifying w(w + 3) + 204 = (2w + 6)(w + -1) Reorder the terms: w(3 + w) + 204 = (2w + 6)(w + -1) (3 * w + w * w) + 204 = (2w + 6)(w + -1) (3w + w2) + 204 = (2w + 6)(w + -1) Reorder the terms: 204 + 3w + w2 = (2w + 6)(w + -1) Reorder the terms: 204 + 3w + w2 = (6 + 2w)(w + -1) Reorder the terms: 204 + 3w + w2 = (6 + 2w)(-1 + w) Multiply (6 + 2w) * (-1 + w) 204 + 3w + w2 = (6(-1 + w) + 2w * (-1 + w)) 204 + 3w + w2 = ((-1 * 6 + w * 6) + 2w * (-1 + w)) 204 + 3w + w2 = ((-6 + 6w) + 2w * (-1 + w)) 204 + 3w + w2 = (-6 + 6w + (-1 * 2w + w * 2w)) 204 + 3w + w2 = (-6 + 6w + (-2w + 2w2)) Combine like terms: 6w + -2w = 4w 204 + 3w + w2 = (-6 + 4w + 2w2) Solving 204 + 3w + w2 = -6 + 4w + 2w2 Solving for variable 'w'. Reorder the terms: 204 + 6 + 3w + -4w + w2 + -2w2 = -6 + 4w + 2w2 + 6 + -4w + -2w2 Combine like terms: 204 + 6 = 210 210 + 3w + -4w + w2 + -2w2 = -6 + 4w + 2w2 + 6 + -4w + -2w2 Combine like terms: 3w + -4w = -1w 210 + -1w + w2 + -2w2 = -6 + 4w + 2w2 + 6 + -4w + -2w2 Combine like terms: w2 + -2w2 = -1w2 210 + -1w + -1w2 = -6 + 4w + 2w2 + 6 + -4w + -2w2 Reorder the terms: 210 + -1w + -1w2 = -6 + 6 + 4w + -4w + 2w2 + -2w2 Combine like terms: -6 + 6 = 0 210 + -1w + -1w2 = 0 + 4w + -4w + 2w2 + -2w2 210 + -1w + -1w2 = 4w + -4w + 2w2 + -2w2 Combine like terms: 4w + -4w = 0 210 + -1w + -1w2 = 0 + 2w2 + -2w2 210 + -1w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 210 + -1w + -1w2 = 0 Factor a trinomial. (14 + -1w)(15 + w) = 0Subproblem 1
Set the factor '(14 + -1w)' equal to zero and attempt to solve: Simplifying 14 + -1w = 0 Solving 14 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1w = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1w = 0 + -14 -1w = 0 + -14 Combine like terms: 0 + -14 = -14 -1w = -14 Divide each side by '-1'. w = 14 Simplifying w = 14Subproblem 2
Set the factor '(15 + w)' equal to zero and attempt to solve: Simplifying 15 + w = 0 Solving 15 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + w = 0 + -15 w = 0 + -15 Combine like terms: 0 + -15 = -15 w = -15 Simplifying w = -15Solution
w = {14, -15}
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