Answer:
[tex]\huge\boxed{x=\dfrac{\pi}{4}+k\pi,\ k\in\mathbb{Z}}\\.\qquad\qquad\downarrow\\\huge\boxed{x=45^o+k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]10\tan x=7\tan x+3\qquad\text{subtract}\ 7\tan x\ \text{from both sides}\\\\10\tan x-7\tan x=7\tan x-7\tan x+3\\\\3\tan x=3\qquad\text{divide both sides by 3}\\\\\dfrac{3\tan x}{3}=\dfrac{3}{3}\\\\\tan x=1\Rightarrow\ x=\dfrac{\pi}{4}+k\pi,\ k\in\mathbb{Z}[/tex]
