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Simplifying w(w + 7) + 114 = 2(w + 7)(w + -3) Reorder the terms: w(7 + w) + 114 = 2(w + 7)(w + -3) (7 * w + w * w) + 114 = 2(w + 7)(w + -3) (7w + w2) + 114 = 2(w + 7)(w + -3) Reorder the terms: 114 + 7w + w2 = 2(w + 7)(w + -3) Reorder the terms: 114 + 7w + w2 = 2(7 + w)(w + -3) Reorder the terms: 114 + 7w + w2 = 2(7 + w)(-3 + w) Multiply (7 + w) * (-3 + w) 114 + 7w + w2 = 2(7(-3 + w) + w(-3 + w)) 114 + 7w + w2 = 2((-3 * 7 + w * 7) + w(-3 + w)) 114 + 7w + w2 = 2((-21 + 7w) + w(-3 + w)) 114 + 7w + w2 = 2(-21 + 7w + (-3 * w + w * w)) 114 + 7w + w2 = 2(-21 + 7w + (-3w + w2)) Combine like terms: 7w + -3w = 4w 114 + 7w + w2 = 2(-21 + 4w + w2) 114 + 7w + w2 = (-21 * 2 + 4w * 2 + w2 * 2) 114 + 7w + w2 = (-42 + 8w + 2w2) Solving 114 + 7w + w2 = -42 + 8w + 2w2 Solving for variable 'w'. Reorder the terms: 114 + 42 + 7w + -8w + w2 + -2w2 = -42 + 8w + 2w2 + 42 + -8w + -2w2 Combine like terms: 114 + 42 = 156 156 + 7w + -8w + w2 + -2w2 = -42 + 8w + 2w2 + 42 + -8w + -2w2 Combine like terms: 7w + -8w = -1w 156 + -1w + w2 + -2w2 = -42 + 8w + 2w2 + 42 + -8w + -2w2 Combine like terms: w2 + -2w2 = -1w2 156 + -1w + -1w2 = -42 + 8w + 2w2 + 42 + -8w + -2w2 Reorder the terms: 156 + -1w + -1w2 = -42 + 42 + 8w + -8w + 2w2 + -2w2 Combine like terms: -42 + 42 = 0 156 + -1w + -1w2 = 0 + 8w + -8w + 2w2 + -2w2 156 + -1w + -1w2 = 8w + -8w + 2w2 + -2w2 Combine like terms: 8w + -8w = 0 156 + -1w + -1w2 = 0 + 2w2 + -2w2 156 + -1w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 156 + -1w + -1w2 = 0 Factor a trinomial. (12 + -1w)(13 + w) = 0Subproblem 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 '(13 + w)' equal to zero and attempt to solve: Simplifying 13 + w = 0 Solving 13 + w = 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 + w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + w = 0 + -13 w = 0 + -13 Combine like terms: 0 + -13 = -13 w = -13 Simplifying w = -13Solution
w = {12, -13}
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