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Simplifying 2(w + 3)(w + -1) + -1w(w + 3) = 150 Reorder the terms: 2(3 + w)(w + -1) + -1w(w + 3) = 150 Reorder the terms: 2(3 + w)(-1 + w) + -1w(w + 3) = 150 Multiply (3 + w) * (-1 + w) 2(3(-1 + w) + w(-1 + w)) + -1w(w + 3) = 150 2((-1 * 3 + w * 3) + w(-1 + w)) + -1w(w + 3) = 150 2((-3 + 3w) + w(-1 + w)) + -1w(w + 3) = 150 2(-3 + 3w + (-1 * w + w * w)) + -1w(w + 3) = 150 2(-3 + 3w + (-1w + w2)) + -1w(w + 3) = 150 Combine like terms: 3w + -1w = 2w 2(-3 + 2w + w2) + -1w(w + 3) = 150 (-3 * 2 + 2w * 2 + w2 * 2) + -1w(w + 3) = 150 (-6 + 4w + 2w2) + -1w(w + 3) = 150 Reorder the terms: -6 + 4w + 2w2 + -1w(3 + w) = 150 -6 + 4w + 2w2 + (3 * -1w + w * -1w) = 150 -6 + 4w + 2w2 + (-3w + -1w2) = 150 Reorder the terms: -6 + 4w + -3w + 2w2 + -1w2 = 150 Combine like terms: 4w + -3w = 1w -6 + 1w + 2w2 + -1w2 = 150 Combine like terms: 2w2 + -1w2 = 1w2 -6 + 1w + 1w2 = 150 Solving -6 + 1w + 1w2 = 150 Solving for variable 'w'. Reorder the terms: -6 + -150 + 1w + 1w2 = 150 + -150 Combine like terms: -6 + -150 = -156 -156 + 1w + 1w2 = 150 + -150 Combine like terms: 150 + -150 = 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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