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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. (-9 + -2w)(6 + -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 '(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 = 6Solution
w = {-4.5, 6}
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