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Simplifying (3w + -1)(3w) = 30 Reorder the terms: (-1 + 3w)(3w) = 30 Remove parenthesis around (3w) (-1 + 3w) * 3w = 30 Reorder the terms for easier multiplication: 3w(-1 + 3w) = 30 (-1 * 3w + 3w * 3w) = 30 (-3w + 9w2) = 30 Solving -3w + 9w2 = 30 Solving for variable 'w'. Reorder the terms: -30 + -3w + 9w2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -3w + 9w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -1w + 3w2) = 0 Factor a trinomial. 3((-5 + -3w)(2 + -1w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -3w)' equal to zero and attempt to solve: Simplifying -5 + -3w = 0 Solving -5 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3w = 0 + 5 -3w = 0 + 5 Combine like terms: 0 + 5 = 5 -3w = 5 Divide each side by '-3'. w = -1.666666667 Simplifying w = -1.666666667Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-1.666666667, 2}
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