5u^3-u^2-4u=0

Solution for 5u^3-u^2-4u=0 equation:

Simplifying
5u3 + -1u2 + -4u = 0

Reorder the terms:
-4u + -1u2 + 5u3 = 0

Solving
-4u + -1u2 + 5u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(-4 + -1u + 5u2) = 0

Factor a trinomial.
u((-4 + -5u)(1 + -1u)) = 0

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 = 0
Subproblem 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 = -0.8
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 = {0, -0.8, 1}