(tan*x)(tan*2*x)-1=0

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

Simplifying
(tan * x)(tan * 2x) + -1 = 0

Multiply ant * x
(antx)(tan * 2x) + -1 = 0

Reorder the terms for easier multiplication:
antx(2ant * x) + -1 = 0

Multiply ant * x
antx(2antx) + -1 = 0

Remove parenthesis around (2antx)
antx * 2antx + -1 = 0

Reorder the terms for easier multiplication:
2antx * antx + -1 = 0

Multiply antx * antx
2a2n2t2x2 + -1 = 0

Reorder the terms:
-1 + 2a2n2t2x2 = 0

Solving
-1 + 2a2n2t2x2 = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + 2a2n2t2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2a2n2t2x2 = 0 + 1
2a2n2t2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2a2n2t2x2 = 1

Divide each side by '2n2t2x2'.
a2 = 0.5n-2t-2x-2

Simplifying
a2 = 0.5n-2t-2x-2

Take the square root of each side:
a = {-0.707106781n-1t-1x-1, 0.707106781n-1t-1x-1}