9 sin ^2x = sin x how do I finish solving?

Question

Using factoring I solve this so that x=0 and x=3pi/2. Once I get to this point I'm unsure what to do. I'm told to put the x value in place of sin x and solve but I can't see an example of this. Additionally I'm not sure how to finish solving, I understand that I should get 4 answers because each x value is added to 2pi.

Can someone show me the solution by replacing sin x with the values.

Answer 1

9 sin ² x - sin x = 0
(sin x) (9 sin x - 1) = 0
sin x = 0 , sin x = 1 / 9

From sin x = 0:-
x = 0° , 180° , 360°

From sin x = 1/9:-
x = sin ^(-1) (1/9) which gives answers in 1st and 2nd quadrants. (sorry but I do not have a calculator to hand!)