find all solutions to the equation

7 sin^2x - 14 sin x + 2 = -5

7 sin^2(x) - 14 sin(x) + 2 = -5
Temporarily substitute y in for sin(x) to make it more readable
7y^2 - 14y + 2 = -5
Move the -5 over by adding to both sides
7y^2 - 14y + 7 = 0
Simplicity by dividing both sides by 7 to get
y^2 - 2y + 1 = 0
Factor to get
(y-1)(y-1) = 0
Or y-1 = 0
y = 1
Therefore
Sin(x) = 1
x = pi/2 + 2pi * n where n represents all whole numbers
Final
x = pi/2 + 2pi * n
Hope I helped :)