Solve equationtan^2x-8tanx+12=0

We have to solve the equation: (tan x)^2 - 8 tan x + 12 =
0

let tan x = y

(tan x)^2 - 8
tan x + 12 = 0

=> y^2 - 8y + 12 =
0

=> y^2 - 6y - 2y + 12 =
0

=> y(y -6) - 2( y - 6) =
0

=> ( y - 2)(y - 6) =
0

So  y = 2 and y = 6

As y =
tan x

tan x = 2 and tan x =
6

=> x = arc tan 2 + n*pi and x = arc tan 6 +
n*pi

Therefore the solution
is

x = arc tan 2 + n*pi
and

x = arc tan 6 +
n*pi