3x^4+18x^2=6x^3

Solution for 3x^4+18x^2=6x^3 equation:

Simplifying
3x4 + 18x2 = 6x3

Reorder the terms:
18x2 + 3x4 = 6x3

Solving
18x2 + 3x4 = 6x3

Solving for variable 'x'.

Reorder the terms:
18x2 + -6x3 + 3x4 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
18x2 + -6x3 + 3x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(6 + -2x + x2) = 0

Ignore the factor 3.
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 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -2x + x2 = 0

Solving
6 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -2x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -2x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -2x + x2 = 0 + -6
-2x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-2x + x2 = -6

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -6 + 1

Reorder the terms:
1 + -2x + x2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + -2x + x2 = -5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -5

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}