Solve the trigonometric equation

Question

6cosxsinx - 3cosx - 4sinx + 2=0 for exact solutions in the interval x is more than or equal to 0 and less than or equal to 360°. 

 

I've got it down to 3cosx-2 = 0 or 2sinx-1=0 but not sure where to go from here. 

Answer 1

6cosxsinx - 3cosx -4sinx +2 =0

3cosx(2sinx-1) -2(2sinx -1) =0

(2sinx-1) (3cosx-2)=0

sinx = 1/2 or cosx=2/3

from 0 to 360°, x= 30° or 150° or arccos(2/3) or 360°-arccos(2/3)