Question 1414
From what you wrote this is how I'm interpreting the problem:

{{{((5q^2+12q-9)/(5q^2-22q-15))*((20q^2+12q)/(9q^2))}}}

Hopefully this is the right problem.

After factoring you'll get {{{(((5q-3)(q+3))/((5q+3)(q-5)))*(4q(5q+3)/(9q^2))}}}

After cross canceling the (5q+3) and canceling out a q on the top and bottom of the right fraction you'll get: {{{(((5q-3)(q+3))/(q-5))*(4/(9q))=(4(5q-3)(q+3))/((q-5)(9q))=(20q^2+48q-36)/(9q^2-45q)}}}