25x^3-26x^2-40x=

Solution for 25x^3-26x^2-40x= equation:

Simplifying
25x3 + -26x2 + -40x = 0

Reorder the terms:
-40x + -26x2 + 25x3 = 0

Solving
-40x + -26x2 + 25x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-40 + -26x + 25x2) = 0

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 '(-40 + -26x + 25x2)' equal to zero and attempt to solve:

Simplifying
-40 + -26x + 25x2 = 0

Solving
-40 + -26x + 25x2 = 0

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

Divide each side by '25'.
-1.6 + -1.04x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -1.04x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -1.04x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -1.04x + x2 = 0 + 1.6
-1.04x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-1.04x + x2 = 1.6

The x term is -1.04x.  Take half its coefficient (-0.52).
Square it (0.2704) and add it to both sides.

Add '0.2704' to each side of the equation.
-1.04x + 0.2704 + x2 = 1.6 + 0.2704

Reorder the terms:
0.2704 + -1.04x + x2 = 1.6 + 0.2704

Combine like terms: 1.6 + 0.2704 = 1.8704
0.2704 + -1.04x + x2 = 1.8704

Factor a perfect square on the left side:
(x + -0.52)(x + -0.52) = 1.8704

Calculate the square root of the right side: 1.36762568

Break this problem into two subproblems by setting 
(x + -0.52) equal to 1.36762568 and -1.36762568.

Subproblem 1
x + -0.52 = 1.36762568

Simplifying
x + -0.52 = 1.36762568

Reorder the terms:
-0.52 + x = 1.36762568

Solving
-0.52 + x = 1.36762568

Solving for variable 'x'.

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

Add '0.52' to each side of the equation.
-0.52 + 0.52 + x = 1.36762568 + 0.52

Combine like terms: -0.52 + 0.52 = 0.00
0.00 + x = 1.36762568 + 0.52
x = 1.36762568 + 0.52

Combine like terms: 1.36762568 + 0.52 = 1.88762568
x = 1.88762568

Simplifying
x = 1.88762568

Subproblem 2
x + -0.52 = -1.36762568

Simplifying
x + -0.52 = -1.36762568

Reorder the terms:
-0.52 + x = -1.36762568

Solving
-0.52 + x = -1.36762568

Solving for variable 'x'.

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

Add '0.52' to each side of the equation.
-0.52 + 0.52 + x = -1.36762568 + 0.52

Combine like terms: -0.52 + 0.52 = 0.00
0.00 + x = -1.36762568 + 0.52
x = -1.36762568 + 0.52

Combine like terms: -1.36762568 + 0.52 = -0.84762568
x = -0.84762568

Simplifying
x = -0.84762568

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.88762568, -0.84762568}
Solution
x = {0, 1.88762568, -0.84762568}