Question on factoring? (Need help ASAP!!!)

How do u factor 3cos=cos+1?

3cos x= cos x + 1

3cosx - cosx = 1

cosx(3 - 1) = 1

cosx(2) = 1

cosx = 1/2

x = pi/3 or 5pi/3

or

3cosx = cosx + 1

2cosx = 1

cosx = 1/2

x = pi/3 or 5pi/3

Double the answer and repeat

Lol