3x^4-8000x^3+6000000x^2=0

Solution for 3x^4-8000x^3+6000000x^2=0 equation:

Simplifying
3x4 + -8000x3 + 6000000x2 = 0

Reorder the terms:
6000000x2 + -8000x3 + 3x4 = 0

Solving
6000000x2 + -8000x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6000000 + -8000x + 3x2) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(6000000 + -8000x + 3x2)' equal to zero and attempt to solve:

Simplifying
6000000 + -8000x + 3x2 = 0

Solving
6000000 + -8000x + 3x2 = 0

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

Divide each side by '3'.
2000000 + -2666.666667x + x2 = 0

Move the constant term to the right:

Add '-2000000' to each side of the equation.
2000000 + -2666.666667x + -2000000 + x2 = 0 + -2000000

Reorder the terms:
2000000 + -2000000 + -2666.666667x + x2 = 0 + -2000000

Combine like terms: 2000000 + -2000000 = 0
0 + -2666.666667x + x2 = 0 + -2000000
-2666.666667x + x2 = 0 + -2000000

Combine like terms: 0 + -2000000 = -2000000
-2666.666667x + x2 = -2000000

The x term is -2666.666667x.  Take half its coefficient (-1333.333334).
Square it (1777777.780) and add it to both sides.

Add '1777777.780' to each side of the equation.
-2666.666667x + 1777777.780 + x2 = -2000000 + 1777777.780

Reorder the terms:
1777777.780 + -2666.666667x + x2 = -2000000 + 1777777.780

Combine like terms: -2000000 + 1777777.780 = -222222.22
1777777.780 + -2666.666667x + x2 = -222222.22

Factor a perfect square on the left side:
(x + -1333.333334)(x + -1333.333334) = -222222.22

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}