Question

solve tan(x)(tanx+1)=0

Answer 1

tan x = 0 and tanx+1 = 0,
this is true at x = 0 and x = 135. (Quadrant ASTC negative at 45*3, use trigonometric table for reference.

Answer 2

tan x*(tan x + 1) = 0
If the chosen interval is (0 < x < 2Pi) then, the answers are:
1) tan x = 0 -> x = 0 and x = Pi
2) tan x = -1 -> x = 3Pi/4 and x = 7Pi/4