4cos2(x)=9sin(x)+6,
4-4sin2(x)=9sin(x)+6,
4sin2(x)+9sin(x)+2=0=(4sin(x)+1)(sin(x)+2). Since sine is confined to the interval [-1,1], the only acceptable solution is sin(x)=-¼, and x=-14.4775° or -14° to the nearest degree.
-14°=360-14=346° and 194° are solutions for 0≤x≤360°.