0=25x^3-5x^2+15x

Solution for 0=25x^3-5x^2+15x equation:

Simplifying
0 = 25x3 + -5x2 + 15x

Reorder the terms:
0 = 15x + -5x2 + 25x3

Solving
0 = 15x + -5x2 + 25x3

Solving for variable 'x'.
Remove the zero:
-15x + 5x2 + -25x3 = 15x + -5x2 + 25x3 + -15x + 5x2 + -25x3

Reorder the terms:
-15x + 5x2 + -25x3 = 15x + -15x + -5x2 + 5x2 + 25x3 + -25x3

Combine like terms: 15x + -15x = 0
-15x + 5x2 + -25x3 = 0 + -5x2 + 5x2 + 25x3 + -25x3
-15x + 5x2 + -25x3 = -5x2 + 5x2 + 25x3 + -25x3

Combine like terms: -5x2 + 5x2 = 0
-15x + 5x2 + -25x3 = 0 + 25x3 + -25x3
-15x + 5x2 + -25x3 = 25x3 + -25x3

Combine like terms: 25x3 + -25x3 = 0
-15x + 5x2 + -25x3 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-3 + x + -5x2) = 0

Ignore the factor 5.
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 '(-3 + x + -5x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + -5x2 = 0

Solving
-3 + x + -5x2 = 0

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

Divide each side by '-5'.
0.6 + -0.2x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.2x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.2x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.2x + x2 = 0 + -0.6
-0.2x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.2x + x2 = -0.6

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = -0.6 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = -0.6 + 0.25

Combine like terms: -0.6 + 0.25 = -0.35
0.25 + -0.2x + x2 = -0.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.35

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}