Factoring 30x²+11xy-30y² is not much different than factoring 30x²+11x-30. For
30x²+11x-30, here's a non-traditional approach that might help. Form the equation 30x²+11x-30=0 , and use the quadratic formula (perhaps skip ahead a few sections in your text book to find it). Get x = -6/5 and x = 5/6. Use these numbers to help factor the original polynomial. Start by using the opposite numbers we found x to equal. (x+6/5)(x-5/6). FOILing this, get x²+(11/30)x - 1. Clearly not what we were looking for, but by multiplying by 30 we get the original polynomial.
30(x+6/5)(x-5/6) = 30x²+11x-30. The 30 can be distributed (carefully) into the two binomials, using a factor of 5 in the first and a factor of 6 in the second. This gets us (5x+6)(6x-5). Similarly, the answer to 30x²+11xy-30y² is (5x+6y)(6x-5y).
I'm not sure if this method is easier than trial & error, but it is a bit more concrete.