You can put this solution on YOUR website! Sometimes it is easier to substitute simple y in for the trig function to see how it factors...we can back-substitute later...
Thus let y = sin x for now...then we have
2y^2 + 5y - 3 =
(2y - 1)(y + 3) =
Now back-substitute and get
(2 sin x - 1)(sin x + 3)
