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Simplifying 27w2 + 135w + -8100 = 0 Reorder the terms: -8100 + 135w + 27w2 = 0 Solving -8100 + 135w + 27w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '27'. 27(-300 + 5w + w2) = 0 Factor a trinomial. 27((-20 + -1w)(15 + -1w)) = 0 Ignore the factor 27.Subproblem 1
Set the factor '(-20 + -1w)' equal to zero and attempt to solve: Simplifying -20 + -1w = 0 Solving -20 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1w = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1w = 0 + 20 -1w = 0 + 20 Combine like terms: 0 + 20 = 20 -1w = 20 Divide each side by '-1'. w = -20 Simplifying w = -20Subproblem 2
Set the factor '(15 + -1w)' equal to zero and attempt to solve: Simplifying 15 + -1w = 0 Solving 15 + -1w = 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 + -1w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1w = 0 + -15 -1w = 0 + -15 Combine like terms: 0 + -15 = -15 -1w = -15 Divide each side by '-1'. w = 15 Simplifying w = 15Solution
w = {-20, 15}
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