(3tan^2x-1)(tan^2x-3)=0

Solution for (3tan^2x-1)(tan^2x-3)=0 equation:

Simplifying
(3tan2x + -1)(tan2x + -3) = 0

Reorder the terms:
(-1 + 3an2tx)(tan2x + -3) = 0

Reorder the terms:
(-1 + 3an2tx)(-3 + an2tx) = 0

Multiply (-1 + 3an2tx) * (-3 + an2tx)
(-1(-3 + an2tx) + 3an2tx * (-3 + an2tx)) = 0
((-3 * -1 + an2tx * -1) + 3an2tx * (-3 + an2tx)) = 0
((3 + -1an2tx) + 3an2tx * (-3 + an2tx)) = 0
(3 + -1an2tx + (-3 * 3an2tx + an2tx * 3an2tx)) = 0
(3 + -1an2tx + (-9an2tx + 3a2n4t2x2)) = 0

Combine like terms: -1an2tx + -9an2tx = -10an2tx
(3 + -10an2tx + 3a2n4t2x2) = 0

Solving
3 + -10an2tx + 3a2n4t2x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -3an2tx)(3 + -1an2tx) = 0

Subproblem 1
Set the factor '(1 + -3an2tx)' equal to zero and attempt to solve:

Simplifying
1 + -3an2tx = 0

Solving
1 + -3an2tx = 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 + -3an2tx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3an2tx = 0 + -1
-3an2tx = 0 + -1

Combine like terms: 0 + -1 = -1
-3an2tx = -1

Divide each side by '-3n2tx'.
a = 0.3333333333n-2t-1x-1

Simplifying
a = 0.3333333333n-2t-1x-1
Subproblem 2
Set the factor '(3 + -1an2tx)' equal to zero and attempt to solve:

Simplifying
3 + -1an2tx = 0

Solving
3 + -1an2tx = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1an2tx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1an2tx = 0 + -3
-1an2tx = 0 + -3

Combine like terms: 0 + -3 = -3
-1an2tx = -3

Divide each side by '-1n2tx'.
a = 3n-2t-1x-1

Simplifying
a = 3n-2t-1x-1
Solution
a = {0.3333333333n-2t-1x-1, 3n-2t-1x-1}