10u^3+4u^2-40u=

Solution for 10u^3+4u^2-40u= equation:

Simplifying
10u3 + 4u2 + -40u = 0

Reorder the terms:
-40u + 4u2 + 10u3 = 0

Solving
-40u + 4u2 + 10u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u'.
2u(-20 + 2u + 5u2) = 0

Ignore the factor 2.
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 '(-20 + 2u + 5u2)' equal to zero and attempt to solve:

Simplifying
-20 + 2u + 5u2 = 0

Solving
-20 + 2u + 5u2 = 0

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

Divide each side by '5'.
-4 + 0.4u + u2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.4u + 4 + u2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.4u + u2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.4u + u2 = 0 + 4
0.4u + u2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.4u + u2 = 4

The u term is 0.4u.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4u + 0.04 + u2 = 4 + 0.04

Reorder the terms:
0.04 + 0.4u + u2 = 4 + 0.04

Combine like terms: 4 + 0.04 = 4.04
0.04 + 0.4u + u2 = 4.04

Factor a perfect square on the left side:
(u + 0.2)(u + 0.2) = 4.04

Calculate the square root of the right side: 2.009975124

Break this problem into two subproblems by setting 
(u + 0.2) equal to 2.009975124 and -2.009975124.

Subproblem 1
u + 0.2 = 2.009975124

Simplifying
u + 0.2 = 2.009975124

Reorder the terms:
0.2 + u = 2.009975124

Solving
0.2 + u = 2.009975124

Solving for variable 'u'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + u = 2.009975124 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + u = 2.009975124 + -0.2
u = 2.009975124 + -0.2

Combine like terms: 2.009975124 + -0.2 = 1.809975124
u = 1.809975124

Simplifying
u = 1.809975124

Subproblem 2
u + 0.2 = -2.009975124

Simplifying
u + 0.2 = -2.009975124

Reorder the terms:
0.2 + u = -2.009975124

Solving
0.2 + u = -2.009975124

Solving for variable 'u'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + u = -2.009975124 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + u = -2.009975124 + -0.2
u = -2.009975124 + -0.2

Combine like terms: -2.009975124 + -0.2 = -2.209975124
u = -2.209975124

Simplifying
u = -2.209975124

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.809975124, -2.209975124}
Solution
u = {0, 1.809975124, -2.209975124}