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Simplifying 27 = (2w + -3) * w Reorder the terms: 27 = (-3 + 2w) * w Reorder the terms for easier multiplication: 27 = w(-3 + 2w) 27 = (-3 * w + 2w * w) 27 = (-3w + 2w2) Solving 27 = -3w + 2w2 Solving for variable 'w'. Reorder the terms: 27 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 27 + 3w + -2w2 = 0 + 2w2 + -2w2 27 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 27 + 3w + -2w2 = 0 Factor a trinomial. (9 + -2w)(3 + w) = 0Subproblem 1
Set the factor '(9 + -2w)' equal to zero and attempt to solve: Simplifying 9 + -2w = 0 Solving 9 + -2w = 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 + -2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2w = 0 + -9 -2w = 0 + -9 Combine like terms: 0 + -9 = -9 -2w = -9 Divide each side by '-2'. w = 4.5 Simplifying w = 4.5Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {4.5, -3}
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