Find all solutions in the interval [0,2pi): tan^2x + (sqrt3-1)tanx-sqrt3 = 0

Question

This is for my trig class. Thanks for the help!

Answer 1

Factor,

(tan x + sqrt3)(tan x - 1) = 0

tan x = -sqrt3, => x = 2pi/3, 5pi/3

or

tan x = 1, => x = pi/4, 5pi/4

Answer: x = pi/4, 2pi/3, 5pi/4, 5pi/3