SOLUTION: Solve 12sin^2(w)+7cos(w)−13=0 for all solutions 0 ≤w<2π

4cos(w)-1=0;  3cos(w)-1=0
  4cos(w)=1;    3cos(w)=1
   cos(w)=1/4;   cos(w)=1/3

Those are positive numbers.  The cosine is positive in 
quadrants QI and QIV, so

For cos(w)=1/4,
w = 1.318116072 radians in QI, 2π-1.318116072 = 4.965069235 in QIV

For cos(w)=1/3,
w = 1.230959417 radians in QI, 2π-1.230959417 = 5.05222589 in QIV

Edwin