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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. (-3 + -1w)(9 + -2w) = 0Subproblem 1
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 = -3Subproblem 2
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 = 4.5Solution
w = {-3, 4.5}
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