=40x^3+2600x^2-40x

Solution for =40x^3+2600x^2-40x equation:

Simplifying
0 = 40x3 + 2600x2 + -40x

Reorder the terms:
0 = -40x + 2600x2 + 40x3

Solving
0 = -40x + 2600x2 + 40x3

Solving for variable 'x'.
Remove the zero:
40x + -2600x2 + -40x3 = -40x + 2600x2 + 40x3 + 40x + -2600x2 + -40x3

Reorder the terms:
40x + -2600x2 + -40x3 = -40x + 40x + 2600x2 + -2600x2 + 40x3 + -40x3

Combine like terms: -40x + 40x = 0
40x + -2600x2 + -40x3 = 0 + 2600x2 + -2600x2 + 40x3 + -40x3
40x + -2600x2 + -40x3 = 2600x2 + -2600x2 + 40x3 + -40x3

Combine like terms: 2600x2 + -2600x2 = 0
40x + -2600x2 + -40x3 = 0 + 40x3 + -40x3
40x + -2600x2 + -40x3 = 40x3 + -40x3

Combine like terms: 40x3 + -40x3 = 0
40x + -2600x2 + -40x3 = 0

Factor out the Greatest Common Factor (GCF), '40x'.
40x(1 + -65x + -1x2) = 0

Ignore the factor 40.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + -65x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + -65x + -1x2 = 0

Solving
1 + -65x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 65x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 65x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 65x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 65x + x2 = 0 + 1
65x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
65x + x2 = 1

The x term is 65x.  Take half its coefficient (32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
65x + 1056.25 + x2 = 1 + 1056.25

Reorder the terms:
1056.25 + 65x + x2 = 1 + 1056.25

Combine like terms: 1 + 1056.25 = 1057.25
1056.25 + 65x + x2 = 1057.25

Factor a perfect square on the left side:
(x + 32.5)(x + 32.5) = 1057.25

Calculate the square root of the right side: 32.515380976

Break this problem into two subproblems by setting 
(x + 32.5) equal to 32.515380976 and -32.515380976.

Subproblem 1
x + 32.5 = 32.515380976

Simplifying
x + 32.5 = 32.515380976

Reorder the terms:
32.5 + x = 32.515380976

Solving
32.5 + x = 32.515380976

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = 32.515380976 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = 32.515380976 + -32.5
x = 32.515380976 + -32.5

Combine like terms: 32.515380976 + -32.5 = 0.015380976
x = 0.015380976

Simplifying
x = 0.015380976

Subproblem 2
x + 32.5 = -32.515380976

Simplifying
x + 32.5 = -32.515380976

Reorder the terms:
32.5 + x = -32.515380976

Solving
32.5 + x = -32.515380976

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = -32.515380976 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = -32.515380976 + -32.5
x = -32.515380976 + -32.5

Combine like terms: -32.515380976 + -32.5 = -65.015380976
x = -65.015380976

Simplifying
x = -65.015380976

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.015380976, -65.015380976}
Solution
x = {0, 0.015380976, -65.015380976}