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Simplifying (2w + 5) * w = 12 Reorder the terms: (5 + 2w) * w = 12 Reorder the terms for easier multiplication: w(5 + 2w) = 12 (5 * w + 2w * w) = 12 (5w + 2w2) = 12 Solving 5w + 2w2 = 12 Solving for variable 'w'. Reorder the terms: -12 + 5w + 2w2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 5w + 2w2 = 0 Factor a trinomial. (-4 + -1w)(3 + -2w) = 0Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. w = -4 Simplifying w = -4Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {-4, 1.5}
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