How do you factor tan^2x-3tanx-2

Let tanx = y or just use it as a variable

tan^2x - 3tanx - 2

a = 1, b = - 3, c = - 3

quadratic formula

tanx = [-b + sqrt (b^2 - 4 ac) ] / 2 a

= [ 3 + sqrt (9 + 12) ] / 2 = 3.56

tanx = [-b - sqrt (b^2 - 4 ac) ] / 2 a

= [ 3 - sqrt (9 + 12) ] / 2 = - 0.56

x = 1st or 3rd quadrant

x = tan^-1 (3.56) = 74.3 (1st)

x = 180 + 74.3 (3rd)

x = tan^-1 (-0.56) two options either 2nd quarter or 4th quadrant

x = 180 - 29.2 (2nd)

x = 360 - 29.2 (4th)