6cos^2(w)+cos(w)-1=0, 0<=w<2pi, w?

This factors as (3cos(w) - 1)(2cos(w) + 1) = 0

 

so cos(w) = 1/3  or  cos(w) = -1/2

 

cos(w) = 1/3 ⇒  w = 70.529° or w = 289.471°

 

cos(w) = -1/2 ⇒   w = 120°  or w = 240°