Find the general solution of this equation

2tan^4 x - tan^2 x -15 = 0

how to find the general solution of this equation??

2tan^4 x - tan^2 x -15 = 0
let y = tan^2 x
2y^2 - y - 15 = 0
(2y + 5)(y - 3) = 0
y = -5/2 , 3
tan^2 x = -5/2 => reject(complex roots)
tan^2 x = 3
x = -π/3 + kπ => k an integer
x = π/3 + kπ => k an integer

the roots are -1 and 1.
the expression you gave can be factored into (tan^2x-3)(2tan^2x+5) = 0
set each piece to 0
for the first part tan^2x=3
we graph both of these and see that the line of x=3 intersects at 1, and -1.
consider the next part 2tan^2 x =-5
doing the same procedure we see they never touch.
hence the only solyutions are -1 and 1

(2 tan^2 x + 5)(tan^2 x - 3) = 0
2 tan^2 x + 5 = 0 or tan^2 x - 3 = 0
2 tan^2 x = -5..............tan^2 x = 3
No solutions..................tan x = ± √3
......................................… = ± π/3 + nπ