Calculus: Multiplying two power series

How do you do this accurately? I can not find the process in my book and I have hw due in less than two hours:(

f(x) = 5 + 3 x + 3 x^2 + 5 x^3 + ...

and

g(x) = 3 + 2 x + 2 x^2 + 3 x^3 + ...

By multiplying power series, find the first few terms of the series for the product

h(x)=f(x) * g(x) = c_0+c_1 x +c_2 x^2 + c_3 x^3 + ....

I need c1,c2,c3

c1 is 5*2x+3*3x... trying to figure out the rest

c2 is 5*2x^2+3*3x^2*(3x*2x)... i think i have this now

c3 is 5*3x^3+3x^2*2x+3x*2x^2+5*3x^3=42x^3 sorry for asking Q's i end up figuring out:)