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Simplifying 3w(4w + -3)(3w + -1) = 0 Reorder the terms: 3w(-3 + 4w)(3w + -1) = 0 Reorder the terms: 3w(-3 + 4w)(-1 + 3w) = 0 Multiply (-3 + 4w) * (-1 + 3w) 3w(-3(-1 + 3w) + 4w * (-1 + 3w)) = 0 3w((-1 * -3 + 3w * -3) + 4w * (-1 + 3w)) = 0 3w((3 + -9w) + 4w * (-1 + 3w)) = 0 3w(3 + -9w + (-1 * 4w + 3w * 4w)) = 0 3w(3 + -9w + (-4w + 12w2)) = 0 Combine like terms: -9w + -4w = -13w 3w(3 + -13w + 12w2) = 0 (3 * 3w + -13w * 3w + 12w2 * 3w) = 0 (9w + -39w2 + 36w3) = 0 Solving 9w + -39w2 + 36w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3w'. 3w(3 + -13w + 12w2) = 0 Factor a trinomial. 3w((1 + -3w)(3 + -4w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(1 + -3w)' equal to zero and attempt to solve: Simplifying 1 + -3w = 0 Solving 1 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3w = 0 + -1 -3w = 0 + -1 Combine like terms: 0 + -1 = -1 -3w = -1 Divide each side by '-3'. w = 0.3333333333 Simplifying w = 0.3333333333Subproblem 3
Set the factor '(3 + -4w)' equal to zero and attempt to solve: Simplifying 3 + -4w = 0 Solving 3 + -4w = 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 + -4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4w = 0 + -3 -4w = 0 + -3 Combine like terms: 0 + -3 = -3 -4w = -3 Divide each side by '-4'. w = 0.75 Simplifying w = 0.75Solution
w = {0, 0.3333333333, 0.75}
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