The equation can be factorised:
4sin2t(3cos3t+5)-(3cos3t+5)=0=(4sin2t-1)(3cos3t+5)=0
Therefore 4sin2t=1 or 3cos3t=-5. cos cannot exceed 1 or be less than -1, so the second option is not a solution.
sin2t=0.25, so 2t=14.4775 degrees (approx) and t=7.24 degrees, also 187.24, 367.24, etc.
sin(180-2t)=0.25, so 180-2t=14.4775, 2t=180-14.4775=165.5225, t=82.76 degrees, also 262.76, 442.76, etc.
Adding or subtracting 180 degrees to these angles generates more solutions because of the periodic nature of sine.