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Simplifying 2(w + 3)(w + -1) + -1w(w + 3) = 84 Reorder the terms: 2(3 + w)(w + -1) + -1w(w + 3) = 84 Reorder the terms: 2(3 + w)(-1 + w) + -1w(w + 3) = 84 Multiply (3 + w) * (-1 + w) 2(3(-1 + w) + w(-1 + w)) + -1w(w + 3) = 84 2((-1 * 3 + w * 3) + w(-1 + w)) + -1w(w + 3) = 84 2((-3 + 3w) + w(-1 + w)) + -1w(w + 3) = 84 2(-3 + 3w + (-1 * w + w * w)) + -1w(w + 3) = 84 2(-3 + 3w + (-1w + w2)) + -1w(w + 3) = 84 Combine like terms: 3w + -1w = 2w 2(-3 + 2w + w2) + -1w(w + 3) = 84 (-3 * 2 + 2w * 2 + w2 * 2) + -1w(w + 3) = 84 (-6 + 4w + 2w2) + -1w(w + 3) = 84 Reorder the terms: -6 + 4w + 2w2 + -1w(3 + w) = 84 -6 + 4w + 2w2 + (3 * -1w + w * -1w) = 84 -6 + 4w + 2w2 + (-3w + -1w2) = 84 Reorder the terms: -6 + 4w + -3w + 2w2 + -1w2 = 84 Combine like terms: 4w + -3w = 1w -6 + 1w + 2w2 + -1w2 = 84 Combine like terms: 2w2 + -1w2 = 1w2 -6 + 1w + 1w2 = 84 Solving -6 + 1w + 1w2 = 84 Solving for variable 'w'. Reorder the terms: -6 + -84 + 1w + 1w2 = 84 + -84 Combine like terms: -6 + -84 = -90 -90 + 1w + 1w2 = 84 + -84 Combine like terms: 84 + -84 = 0 -90 + 1w + 1w2 = 0 Factor a trinomial. (-10 + -1w)(9 + -1w) = 0Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve: Simplifying -10 + -1w = 0 Solving -10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1w = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1w = 0 + 10 -1w = 0 + 10 Combine like terms: 0 + 10 = 10 -1w = 10 Divide each side by '-1'. w = -10 Simplifying w = -10Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Solution
w = {-10, 9}
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