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Simplifying (2w + 3) * w = 54 Reorder the terms: (3 + 2w) * w = 54 Reorder the terms for easier multiplication: w(3 + 2w) = 54 (3 * w + 2w * w) = 54 (3w + 2w2) = 54 Solving 3w + 2w2 = 54 Solving for variable 'w'. Reorder the terms: -54 + 3w + 2w2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 3w + 2w2 = 0 Factor a trinomial. (-6 + -1w)(9 + -2w) = 0Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 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 = {-6, 4.5}
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