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Simplifying 12 = 3w2 + -5w Reorder the terms: 12 = -5w + 3w2 Solving 12 = -5w + 3w2 Solving for variable 'w'. Reorder the terms: 12 + 5w + -3w2 = -5w + 5w + 3w2 + -3w2 Combine like terms: -5w + 5w = 0 12 + 5w + -3w2 = 0 + 3w2 + -3w2 12 + 5w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 12 + 5w + -3w2 = 0 Factor a trinomial. (3 + -1w)(4 + 3w) = 0Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Subproblem 2
Set the factor '(4 + 3w)' equal to zero and attempt to solve: Simplifying 4 + 3w = 0 Solving 4 + 3w = 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 + 3w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3w = 0 + -4 3w = 0 + -4 Combine like terms: 0 + -4 = -4 3w = -4 Divide each side by '3'. w = -1.333333333 Simplifying w = -1.333333333Solution
w = {3, -1.333333333}
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