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Simplifying (w + -3)(w + 5) = 9 Reorder the terms: (-3 + w)(w + 5) = 9 Reorder the terms: (-3 + w)(5 + w) = 9 Multiply (-3 + w) * (5 + w) (-3(5 + w) + w(5 + w)) = 9 ((5 * -3 + w * -3) + w(5 + w)) = 9 ((-15 + -3w) + w(5 + w)) = 9 (-15 + -3w + (5 * w + w * w)) = 9 (-15 + -3w + (5w + w2)) = 9 Combine like terms: -3w + 5w = 2w (-15 + 2w + w2) = 9 Solving -15 + 2w + w2 = 9 Solving for variable 'w'. Reorder the terms: -15 + -9 + 2w + w2 = 9 + -9 Combine like terms: -15 + -9 = -24 -24 + 2w + w2 = 9 + -9 Combine like terms: 9 + -9 = 0 -24 + 2w + w2 = 0 Factor a trinomial. (-6 + -1w)(4 + -1w) = 0Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-6, 4}
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