Question

find all solutions of 7 sin^2 x - 14 sin x + 2 = -5

Answer 1

It may not be immediately obvious, but this is a quadratic equation.
Substituting y for sin x,

we have 7y^2 - 14y + 7 = 0

You could simplify this further by dividing all 4 terms by 7. Try it and see what happens.

Your result?

Answer 2

y+2 y-1
y=-2 y=1
so sin=-2,1?

Answer 3

Have you checked your answers? Substitute y=-2 and y=-1 into the equation in y.