x^4=3x^3-6x^2

Solution for x^4=3x^3-6x^2 equation:

Simplifying
x4 = 3x3 + -6x2

Reorder the terms:
x4 = -6x2 + 3x3

Solving
x4 = -6x2 + 3x3

Solving for variable 'x'.

Reorder the terms:
6x2 + -3x3 + x4 = -6x2 + 3x3 + 6x2 + -3x3

Reorder the terms:
6x2 + -3x3 + x4 = -6x2 + 6x2 + 3x3 + -3x3

Combine like terms: -6x2 + 6x2 = 0
6x2 + -3x3 + x4 = 0 + 3x3 + -3x3
6x2 + -3x3 + x4 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
6x2 + -3x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + -3x + x2) = 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 '(6 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -3x + x2 = 0

Solving
6 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -3x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3x + x2 = 0 + -6
-3x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3x + x2 = -6

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3x + x2 = -3.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -3.75

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}