sequences and series - How to compute $sum_{n=0}^{infty}left(frac{4}{(-3)^n} - frac{3}{3^n}right)$?

I'm currently trying to compute the following series (found on page 65 of this textbook):

$$\sum_{n=0}^{\infty}\left(\frac{4}{(-3)^n} - \frac{3}{3^n}\right)$$

I've tried to somehow transform it into a geometric series (which I'm fairly sure is the strategy for this series), but I've been unable to. Any help in solving this would be appreciated (though I'd prefer a hint over a solid answer).

Answer

Hint:

$$\frac{4}{(-3)^n} - \frac 3 {3^n} = 4 \left(- \frac 1 3\right)^n - 3 \left(\frac 1 3\right)^n$$