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Simplifying (2w + 6)(2w + 9) = 54 Reorder the terms: (6 + 2w)(2w + 9) = 54 Reorder the terms: (6 + 2w)(9 + 2w) = 54 Multiply (6 + 2w) * (9 + 2w) (6(9 + 2w) + 2w * (9 + 2w)) = 54 ((9 * 6 + 2w * 6) + 2w * (9 + 2w)) = 54 ((54 + 12w) + 2w * (9 + 2w)) = 54 (54 + 12w + (9 * 2w + 2w * 2w)) = 54 (54 + 12w + (18w + 4w2)) = 54 Combine like terms: 12w + 18w = 30w (54 + 30w + 4w2) = 54 Add '-54' to each side of the equation. 54 + 30w + -54 + 4w2 = 54 + -54 Reorder the terms: 54 + -54 + 30w + 4w2 = 54 + -54 Combine like terms: 54 + -54 = 0 0 + 30w + 4w2 = 54 + -54 30w + 4w2 = 54 + -54 Combine like terms: 54 + -54 = 0 30w + 4w2 = 0 Solving 30w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(15 + 2w) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(15 + 2w)' equal to zero and attempt to solve: Simplifying 15 + 2w = 0 Solving 15 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 2w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2w = 0 + -15 2w = 0 + -15 Combine like terms: 0 + -15 = -15 2w = -15 Divide each side by '2'. w = -7.5 Simplifying w = -7.5Solution
w = {0, -7.5}
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