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Simplifying 3w2 + -5w2 + -27w + 45 = 0 Reorder the terms: 45 + -27w + 3w2 + -5w2 = 0 Combine like terms: 3w2 + -5w2 = -2w2 45 + -27w + -2w2 = 0 Solving 45 + -27w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (3 + -2w)(15 + w) = 0Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(15 + w)' equal to zero and attempt to solve: Simplifying 15 + w = 0 Solving 15 + w = 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 + w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + w = 0 + -15 w = 0 + -15 Combine like terms: 0 + -15 = -15 w = -15 Simplifying w = -15Solution
w = {1.5, -15}
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