6a^4+6a^2b^2-252b^4=0

Solution for 6a^4+6a^2b^2-252b^4=0 equation:

Simplifying
6a4 + 6a2b2 + -252b4 = 0

Reorder the terms:
6a2b2 + 6a4 + -252b4 = 0

Solving
6a2b2 + 6a4 + -252b4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(a2b2 + a4 + -42b4) = 0

Factor a trinomial.
6((a2 + -6b2)(a2 + 7b2)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(a2 + -6b2)' equal to zero and attempt to solve:

Simplifying
a2 + -6b2 = 0

Solving
a2 + -6b2 = 0

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

Add '6b2' to each side of the equation.
a2 + -6b2 + 6b2 = 0 + 6b2

Combine like terms: -6b2 + 6b2 = 0
a2 + 0 = 0 + 6b2
a2 = 0 + 6b2
Remove the zero:
a2 = 6b2

Simplifying
a2 = 6b2

Take the square root of each side:
a = {-2.449489743b, 2.449489743b}
Subproblem 2
Set the factor '(a2 + 7b2)' equal to zero and attempt to solve:

Simplifying
a2 + 7b2 = 0

Solving
a2 + 7b2 = 0

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

Add '-7b2' to each side of the equation.
a2 + 7b2 + -7b2 = 0 + -7b2

Combine like terms: 7b2 + -7b2 = 0
a2 + 0 = 0 + -7b2
a2 = 0 + -7b2
Remove the zero:
a2 = -7b2

Simplifying
a2 = -7b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {-2.449489743b, 2.449489743b}