(12*tan^2x-4)(tan^2x-3)=0

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Solution for (12*tan^2x-4)(tan^2x-3)=0 equation: 


Simplifying
(12tan2x + -4)(tan2x + -3) = 0

Reorder the terms:
(-4 + 12an2tx)(tan2x + -3) = 0

Reorder the terms:
(-4 + 12an2tx)(-3 + an2tx) = 0

Multiply (-4 + 12an2tx) * (-3 + an2tx)
(-4(-3 + an2tx) + 12an2tx * (-3 + an2tx)) = 0
((-3 * -4 + an2tx * -4) + 12an2tx * (-3 + an2tx)) = 0
((12 + -4an2tx) + 12an2tx * (-3 + an2tx)) = 0
(12 + -4an2tx + (-3 * 12an2tx + an2tx * 12an2tx)) = 0
(12 + -4an2tx + (-36an2tx + 12a2n4t2x2)) = 0

Combine like terms: -4an2tx + -36an2tx = -40an2tx
(12 + -40an2tx + 12a2n4t2x2) = 0

Solving
12 + -40an2tx + 12a2n4t2x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -10an2tx + 3a2n4t2x2) = 0

Factor a trinomial.
4((1 + -3an2tx)(3 + -1an2tx)) = 0

Ignore the factor 4.

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}

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