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Simplifying (2w + 18)(w + -4) + -84 = w(w + 9) Reorder the terms: (18 + 2w)(w + -4) + -84 = w(w + 9) Reorder the terms: (18 + 2w)(-4 + w) + -84 = w(w + 9) Multiply (18 + 2w) * (-4 + w) (18(-4 + w) + 2w * (-4 + w)) + -84 = w(w + 9) ((-4 * 18 + w * 18) + 2w * (-4 + w)) + -84 = w(w + 9) ((-72 + 18w) + 2w * (-4 + w)) + -84 = w(w + 9) (-72 + 18w + (-4 * 2w + w * 2w)) + -84 = w(w + 9) (-72 + 18w + (-8w + 2w2)) + -84 = w(w + 9) Combine like terms: 18w + -8w = 10w (-72 + 10w + 2w2) + -84 = w(w + 9) Reorder the terms: -72 + -84 + 10w + 2w2 = w(w + 9) Combine like terms: -72 + -84 = -156 -156 + 10w + 2w2 = w(w + 9) Reorder the terms: -156 + 10w + 2w2 = w(9 + w) -156 + 10w + 2w2 = (9 * w + w * w) -156 + 10w + 2w2 = (9w + w2) Solving -156 + 10w + 2w2 = 9w + w2 Solving for variable 'w'. Reorder the terms: -156 + 10w + -9w + 2w2 + -1w2 = 9w + w2 + -9w + -1w2 Combine like terms: 10w + -9w = 1w -156 + 1w + 2w2 + -1w2 = 9w + w2 + -9w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -156 + 1w + 1w2 = 9w + w2 + -9w + -1w2 Reorder the terms: -156 + 1w + 1w2 = 9w + -9w + w2 + -1w2 Combine like terms: 9w + -9w = 0 -156 + 1w + 1w2 = 0 + w2 + -1w2 -156 + 1w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -156 + 1w + 1w2 = 0 Factor a trinomial. (-13 + -1w)(12 + -1w) = 0Subproblem 1
Set the factor '(-13 + -1w)' equal to zero and attempt to solve: Simplifying -13 + -1w = 0 Solving -13 + -1w = 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 + -1w = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1w = 0 + 13 -1w = 0 + 13 Combine like terms: 0 + 13 = 13 -1w = 13 Divide each side by '-1'. w = -13 Simplifying w = -13Subproblem 2
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 = 12Solution
w = {-13, 12}
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