Find values of x in the interval 0<x<360 degrees. For which 5sin^2(x) + 5 sin(x) +4 cos^2(x)=0

This question is split up into two parts.
Firstly recall the trigonometric identities you know, the trick here is to eliminate one of the squared terms. Using 4sin^2(x) +4cos^2(x) = 4, the cos term is eliminated.
Rearranging this equation leaves you with a strange quadratic equation, but if you pretend sin is x it actually looks quite simple and can be solved like a simple quadratic. Solve like this and replace x for sin and the solution follows