@gari,
it is simply homogenous recurrence equation,
corresponding polynomial is,
x2-9x+20=0
roots are x=4 and x=5
T(n) = a4n + b5n
now to find constants 'a' and 'b' use T(0)=-3 and T(1)=-10
you will get a=-5 and b=2,
therefore final solution to above homogenous equation is, $T(n)=-5.4^{n}+2.5^{n}$
it can also be solved by substitution, but it will take time..
for these types of qsns(homogenous recurrence relations), directly use straightforward approach.