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Simplifying (2w + 3) * w = 27 Reorder the terms: (3 + 2w) * w = 27 Reorder the terms for easier multiplication: w(3 + 2w) = 27 (3 * w + 2w * w) = 27 (3w + 2w2) = 27 Solving 3w + 2w2 = 27 Solving for variable 'w'. Reorder the terms: -27 + 3w + 2w2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 3w + 2w2 = 0 Factor a trinomial. (-9 + -2w)(3 + -1w) = 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 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {-4.5, 3}
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