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

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

Simplifying
2u3 + 5u2 + -4u = 0

Reorder the terms:
-4u + 5u2 + 2u3 = 0

Solving
-4u + 5u2 + 2u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(-4 + 5u + 2u2) = 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 + 2u2)' equal to zero and attempt to solve:

Simplifying
-4 + 5u + 2u2 = 0

Solving
-4 + 5u + 2u2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2 + 2.5u + u2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.5u + 2 + u2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.5u + u2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.5u + u2 = 0 + 2
2.5u + u2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.5u + u2 = 2

The u term is 2.5u.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5u + 1.5625 + u2 = 2 + 1.5625

Reorder the terms:
1.5625 + 2.5u + u2 = 2 + 1.5625

Combine like terms: 2 + 1.5625 = 3.5625
1.5625 + 2.5u + u2 = 3.5625

Factor a perfect square on the left side:
(u + 1.25)(u + 1.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(u + 1.25) equal to 1.887458609 and -1.887458609.

Subproblem 1
u + 1.25 = 1.887458609

Simplifying
u + 1.25 = 1.887458609

Reorder the terms:
1.25 + u = 1.887458609

Solving
1.25 + u = 1.887458609

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-1.25' to each side of the equation.
1.25 + -1.25 + u = 1.887458609 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + u = 1.887458609 + -1.25
u = 1.887458609 + -1.25

Combine like terms: 1.887458609 + -1.25 = 0.637458609
u = 0.637458609

Simplifying
u = 0.637458609

Subproblem 2
u + 1.25 = -1.887458609

Simplifying
u + 1.25 = -1.887458609

Reorder the terms:
1.25 + u = -1.887458609

Solving
1.25 + u = -1.887458609

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-1.25' to each side of the equation.
1.25 + -1.25 + u = -1.887458609 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + u = -1.887458609 + -1.25
u = -1.887458609 + -1.25

Combine like terms: -1.887458609 + -1.25 = -3.137458609
u = -3.137458609

Simplifying
u = -3.137458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.637458609, -3.137458609}
Solution
u = {0, 0.637458609, -3.137458609}