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Simplifying 9u(5u + 4)(2u + -1) = 0 Reorder the terms: 9u(4 + 5u)(2u + -1) = 0 Reorder the terms: 9u(4 + 5u)(-1 + 2u) = 0 Multiply (4 + 5u) * (-1 + 2u) 9u(4(-1 + 2u) + 5u * (-1 + 2u)) = 0 9u((-1 * 4 + 2u * 4) + 5u * (-1 + 2u)) = 0 9u((-4 + 8u) + 5u * (-1 + 2u)) = 0 9u(-4 + 8u + (-1 * 5u + 2u * 5u)) = 0 9u(-4 + 8u + (-5u + 10u2)) = 0 Combine like terms: 8u + -5u = 3u 9u(-4 + 3u + 10u2) = 0 (-4 * 9u + 3u * 9u + 10u2 * 9u) = 0 (-36u + 27u2 + 90u3) = 0 Solving -36u + 27u2 + 90u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '9u'. 9u(-4 + 3u + 10u2) = 0 Factor a trinomial. 9u((-4 + -5u)(1 + -2u)) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0Subproblem 2
Set the factor '(-4 + -5u)' equal to zero and attempt to solve: Simplifying -4 + -5u = 0 Solving -4 + -5u = 0 Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5u = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5u = 0 + 4 -5u = 0 + 4 Combine like terms: 0 + 4 = 4 -5u = 4 Divide each side by '-5'. u = -0.8 Simplifying u = -0.8Subproblem 3
Set the factor '(1 + -2u)' equal to zero and attempt to solve: Simplifying 1 + -2u = 0 Solving 1 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2u = 0 + -1 -2u = 0 + -1 Combine like terms: 0 + -1 = -1 -2u = -1 Divide each side by '-2'. u = 0.5 Simplifying u = 0.5Solution
u = {0, -0.8, 0.5}
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