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Simplifying 54 = (3 + 2w) * w Reorder the terms for easier multiplication: 54 = w(3 + 2w) 54 = (3 * w + 2w * w) 54 = (3w + 2w2) Solving 54 = 3w + 2w2 Solving for variable 'w'. Reorder the terms: 54 + -3w + -2w2 = 3w + -3w + 2w2 + -2w2 Combine like terms: 3w + -3w = 0 54 + -3w + -2w2 = 0 + 2w2 + -2w2 54 + -3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 54 + -3w + -2w2 = 0 Factor a trinomial. (9 + -2w)(6 + 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 '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 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 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Solution
w = {4.5, -6}
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