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Simplifying 135 = w(w + 6) Reorder the terms: 135 = w(6 + w) 135 = (6 * w + w * w) 135 = (6w + w2) Solving 135 = 6w + w2 Solving for variable 'w'. Reorder the terms: 135 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 135 + -6w + -1w2 = 0 + w2 + -1w2 135 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 135 + -6w + -1w2 = 0 Factor a trinomial. (9 + -1w)(15 + w) = 0Subproblem 1
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 = 9Subproblem 2
Set the factor '(15 + w)' equal to zero and attempt to solve: Simplifying 15 + w = 0 Solving 15 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + w = 0 + -15 w = 0 + -15 Combine like terms: 0 + -15 = -15 w = -15 Simplifying w = -15Solution
w = {9, -15}
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