2sin² x + 3cos²x + 2sin x = 0 заменить 3cos²x= 3*(1- sin²х

sin²x + cos²x =1

cos²x = 1 - sin²x

3 cos²x = 3(1 - sin²x)

2sin² x + 3cos²x + 2sin x = 0 

2sin²x + 1 - sin²x + 2 sin x = 0

1 + 2 sin x =0

2 sin x = -1

sin x = -0,5

x = -π/6

x[1]=11π/6 + 2kπ

x[2]=7π/6 + 2kπ