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Simplifying 324 = (3 + 2w)(w) Reorder the terms for easier multiplication: 324 = w(3 + 2w) 324 = (3 * w + 2w * w) 324 = (3w + 2w2) Solving 324 = 3w + 2w2 Solving for variable 'w'. Reorder the terms: 324 + -3w + -2w2 = 3w + -3w + 2w2 + -2w2 Combine like terms: 3w + -3w = 0 324 + -3w + -2w2 = 0 + 2w2 + -2w2 324 + -3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 324 + -3w + -2w2 = 0 Factor a trinomial. (12 + -1w)(27 + 2w) = 0Subproblem 1
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 = 12Subproblem 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 = {12, -13.5}
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