2 tan x + ? (12) = 0

[amy-lee]

Solve the following for x: 2 tan x + ? (12) = 0 where 0 < x < 2pi.
I'm not sure how to begin solving this equation.

 

[galactus]

First, rewrite as $\displaystyle tan(x)=\frac{-\sqrt{12}}{2}$

$\displaystyle \frac{-\sqrt{12}}{2}=-\sqrt{3}$

$\displaystyle tan(x)=-\sqrt{3}$

$\displaystyle x=c{\pi}-\frac{\pi}{3}$