6a^4=2a^2

Solution for 6a^4=2a^2 equation:

Simplifying
6a4 = 2a2

Solving
6a4 = 2a2

Solving for variable 'a'.

Reorder the terms:
-2a2 + 6a4 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
-2a2 + 6a4 = 0

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(-1 + 3a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-1 + 3a2)' equal to zero and attempt to solve:

Simplifying
-1 + 3a2 = 0

Solving
-1 + 3a2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3a2 = 0 + 1
3a2 = 0 + 1

Combine like terms: 0 + 1 = 1
3a2 = 1

Divide each side by '3'.
a2 = 0.3333333333

Simplifying
a2 = 0.3333333333

Take the square root of each side:
a = {-0.577350269, 0.577350269}
Solution
a = {0, -0.577350269, 0.577350269}