24a^2-8a^4+28a^6=0

Solution for 24a^2-8a^4+28a^6=0 equation:

Simplifying
24a2 + -8a4 + 28a6 = 0

Solving
24a2 + -8a4 + 28a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a2'.
4a2(6 + -2a2 + 7a4) = 0

Ignore the factor 4.
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 '(6 + -2a2 + 7a4)' equal to zero and attempt to solve:

Simplifying
6 + -2a2 + 7a4 = 0

Solving
6 + -2a2 + 7a4 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.8571428571 + -0.2857142857a2 + a4 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -0.2857142857a2 + -0.8571428571 + a4 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -0.2857142857a2 + a4 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -0.2857142857a2 + a4 = 0 + -0.8571428571
-0.2857142857a2 + a4 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-0.2857142857a2 + a4 = -0.8571428571

The a term is -0.2857142857a2.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857a2 + 0.02040816328 + a4 = -0.8571428571 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857a2 + a4 = -0.8571428571 + 0.02040816328

Combine like terms: -0.8571428571 + 0.02040816328 = -0.83673469382
0.02040816328 + -0.2857142857a2 + a4 = -0.83673469382

Factor a perfect square on the left side:
(a2 + -0.1428571429)(a2 + -0.1428571429) = -0.83673469382

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
a = {0}