72a^4-24a^2+2=

Solution for 72a^4-24a^2+2= equation:

Simplifying
72a4 + -24a2 + 2 = 0

Reorder the terms:
2 + -24a2 + 72a4 = 0

Solving
2 + -24a2 + 72a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -12a2 + 36a4) = 0

Factor a trinomial.
2((1 + -6a2)(1 + -6a2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -6a2)' equal to zero and attempt to solve:

Simplifying
1 + -6a2 = 0

Solving
1 + -6a2 = 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 + -6a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6a2 = 0 + -1
-6a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6a2 = -1

Divide each side by '-6'.
a2 = 0.1666666667

Simplifying
a2 = 0.1666666667

Take the square root of each side:
a = {-0.408248291, 0.408248291}
Subproblem 2
Set the factor '(1 + -6a2)' equal to zero and attempt to solve:

Simplifying
1 + -6a2 = 0

Solving
1 + -6a2 = 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 + -6a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6a2 = 0 + -1
-6a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6a2 = -1

Divide each side by '-6'.
a2 = 0.1666666667

Simplifying
a2 = 0.1666666667

Take the square root of each side:
a = {-0.408248291, 0.408248291}
Solution
a = {-0.408248291, 0.408248291, -0.408248291, 0.408248291}