54a^4-36a^2+6=

Solution for 54a^4-36a^2+6= equation:

Simplifying
54a4 + -36a2 + 6 = 0

Reorder the terms:
6 + -36a2 + 54a4 = 0

Solving
6 + -36a2 + 54a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + -6a2 + 9a4) = 0

Factor a trinomial.
6((1 + -3a2)(1 + -3a2)) = 0

Ignore the factor 6.
Subproblem 1
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}
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 = {-0.577350269, 0.577350269, -0.577350269, 0.577350269}