Verified Answer :

HomertheGenius

sin² x + sin x = 0
sin x ( sin x + 1 ) = 0
sin x = 0       or     sin x + 1 = 0
x 1 = kπ,               sin x = -1
k ∈ Z                     x 2 = 3π/2 + 2 kπ,   k ∈ Z

Answer:

sinx =0 + 2πn or

sinx =-1 + 2πn

Step-by-step explanation:

sin2x + sin x = 0

sinx (sinx + 1) = 0

sinx =0, then x=π+2π= π (1+2n) and x=2π + 2πn = 2π (1+n)

 or

sinx +1=0, 

x =-3π/2  + 2πn

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