Find all solutions of the equation in the interval 0 2pi 2 s

Find all solutions of the equation in the interval [0, 2pi) 2 sin^2 x + 3 sin x + 1 = 0

2sin^2(x) + 3sinx + 1 = 0

Split up middle term using the quadratic method :
2sin^2(x) + 2sinx + sinx + 1 = 0

Now factor by grouping :
2sinx(sinx + 1) + 1(sinx + 1) = 0

Now, factor the common snx + 1 term :
(2sinx + 1)(sinx + 1) = 0

Now, by zero factor property, equate each to 0 :
2sinx + 1 = 0 , sinx + 1 =0

sinx = -1/2 and sinx = -1

So, within [0 , 2pi], the answers are :

x = 7pi/6 , 11pi/6 and 3pi/2 ----> ANSWER