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Simplifying 243 = (2w + 9)(w) Reorder the terms: 243 = (9 + 2w)(w) Reorder the terms for easier multiplication: 243 = w(9 + 2w) 243 = (9 * w + 2w * w) 243 = (9w + 2w2) Solving 243 = 9w + 2w2 Solving for variable 'w'. Reorder the terms: 243 + -9w + -2w2 = 9w + -9w + 2w2 + -2w2 Combine like terms: 9w + -9w = 0 243 + -9w + -2w2 = 0 + 2w2 + -2w2 243 + -9w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 243 + -9w + -2w2 = 0 Factor a trinomial. (9 + -1w)(27 + 2w) = 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 '(27 + 2w)' equal to zero and attempt to solve: Simplifying 27 + 2w = 0 Solving 27 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 2w = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 2w = 0 + -27 2w = 0 + -27 Combine like terms: 0 + -27 = -27 2w = -27 Divide each side by '2'. w = -13.5 Simplifying w = -13.5Solution
w = {9, -13.5}
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