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Simplifying 24u3 + 54u2 = 15u Reorder the terms: 54u2 + 24u3 = 15u Solving 54u2 + 24u3 = 15u Solving for variable 'u'. Reorder the terms: -15u + 54u2 + 24u3 = 15u + -15u Combine like terms: 15u + -15u = 0 -15u + 54u2 + 24u3 = 0 Factor out the Greatest Common Factor (GCF), '3u'. 3u(-5 + 18u + 8u2) = 0 Factor a trinomial. 3u((-5 + -2u)(1 + -4u)) = 0 Ignore the factor 3.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 '(-5 + -2u)' equal to zero and attempt to solve: Simplifying -5 + -2u = 0 Solving -5 + -2u = 0 Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2u = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2u = 0 + 5 -2u = 0 + 5 Combine like terms: 0 + 5 = 5 -2u = 5 Divide each side by '-2'. u = -2.5 Simplifying u = -2.5Subproblem 3
Set the factor '(1 + -4u)' equal to zero and attempt to solve: Simplifying 1 + -4u = 0 Solving 1 + -4u = 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 + -4u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4u = 0 + -1 -4u = 0 + -1 Combine like terms: 0 + -1 = -1 -4u = -1 Divide each side by '-4'. u = 0.25 Simplifying u = 0.25Solution
u = {0, -2.5, 0.25}
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