48x^3-60x^2+60x=0

Solution for 48x^3-60x^2+60x=0 equation:

Simplifying
48x3 + -60x2 + 60x = 0

Reorder the terms:
60x + -60x2 + 48x3 = 0

Solving
60x + -60x2 + 48x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(5 + -5x + 4x2) = 0

Ignore the factor 12.
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 '(5 + -5x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + -5x + 4x2 = 0

Solving
5 + -5x + 4x2 = 0

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

Divide each side by '4'.
1.25 + -1.25x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -1.25x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -1.25x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -1.25x + x2 = 0 + -1.25
-1.25x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-1.25x + x2 = -1.25

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -1.25 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -1.25 + 0.390625

Combine like terms: -1.25 + 0.390625 = -0.859375
0.390625 + -1.25x + x2 = -0.859375

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = -0.859375

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}