Hello if someone would be able to show me step by step how t

Hello, if someone would be able to show me step by step how to do this problem so I could better understand it, it would be greatly appreciated.

Use algebraic methods to find all (exact) solutions:

2sin²x+7sinx=4

2sin^2x +7sinx =4

2sin^2x +7sinx -4 =0

solve the quadratic by factorisation:

2sin^2x +8sinx -sinx -4 =0

2sin(sinx +4) -1(sinx +4) =0

(2sinx -1)(sinx+4) =0

sinx= 1/2 ; sinx=-4

Neglect sinx=-4 as sinx>=-1

So, sinx =1/2

x= sin^-1(1/2)

x= pi/6 , pi-pi/6 = pi/6 , 5pi/6

Solution : interval [0, 2pi) x= pi/6 , 5pi/6

General solution : x= pi/6 +2k*pi , 5pi/6 +2k*pi

where k is any integer