18x^2=6x^4

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

Simplifying
18x2 = 6x4

Solving
18x2 = 6x4

Solving for variable 'x'.

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

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

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

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {0, -1.732050808, 1.732050808}