Solve the equation(GS general solution)

Question

5sin^2x-3sinx-2=0

Answer 1

let y = sin x

5 y^2 -3 y - 2 = 0
(5 y +2)(y-1) = 0

y = 1 or y = -2/5
so
sin x = 1 ---> x = 90deg or 90+360 etc
sin x = -2/5 ---> x = -23.6 or 180+23.6 etc