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Simplifying 4u^{6}+ 6u^{5}+ -10u^{4}= 0 Reorder the terms: -10u^{4}+ 6u^{5}+ 4u^{6}= 0 Solving -10u^{4}+ 6u^{5}+ 4u^{6}= 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2u^{4}'. 2u^{4}(-5 + 3u + 2u^{2}) = 0 Factor a trinomial. 2u^{4}((-5 + -2u)(1 + -1u)) = 0 Ignore the factor 2.## Subproblem 1

Set the factor 'u^{4}' equal to zero and attempt to solve: Simplifying u^{4}= 0 Solving u^{4}= 0 Move all terms containing u to the left, all other terms to the right. Simplifying u^{4}= 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.## Subproblem 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 = -2.5## Subproblem 3

Set the factor '(1 + -1u)' equal to zero and attempt to solve: Simplifying 1 + -1u = 0 Solving 1 + -1u = 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 + -1u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1u = 0 + -1 -1u = 0 + -1 Combine like terms: 0 + -1 = -1 -1u = -1 Divide each side by '-1'. u = 1 Simplifying u = 1## Solution

u = {-2.5, 1}

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