24x^3-8x^2+48x=0

Solution for 24x^3-8x^2+48x=0 equation:

Simplifying
24x3 + -8x2 + 48x = 0

Reorder the terms:
48x + -8x2 + 24x3 = 0

Solving
48x + -8x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(6 + -1x + 3x2) = 0

Ignore the factor 8.
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 '(6 + -1x + 3x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x + 3x2 = 0

Solving
6 + -1x + 3x2 = 0

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

Divide each side by '3'.
2 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -0.3333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -0.3333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -0.3333333333x + x2 = 0 + -2
-0.3333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-0.3333333333x + x2 = -2

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = -2 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = -2 + 0.02777777779

Combine like terms: -2 + 0.02777777779 = -1.97222222221
0.02777777779 + -0.3333333333x + x2 = -1.97222222221

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = -1.97222222221

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}