4sinx+2sin2x=5
The easiest way to solve this is to plot y= 5, and y= 4x sin(x) (1 + cos x) and find their intersection points. There isn't a single solution.
x~~2 (3.1416 n+0.42776) and n element Z
x~~2 (3.1416 n+0.62315) and n element Z
x~~2 (3.1416 n-(1.3109+0.5666 i)) and n element Z
x~~2 (3.1416 n-(1.3109-0.5666 i)) and n element Z