0 12 10 0 -12 -20

I calculate the differences, and find it's a 3rd degree polynomial.

An^3+Bn^2+Cn+D

So I know when n=1 the above equation=0, and when n=2, 12, and so on.

So I come up with these 4 equations

a + b+ c+d=0

8a+ 4b+2c+d=12

27a+ 9b+3c+d=10

64a+16b+4c+d=0

Now I have to solve this system of linear equations. I just keep trying and getting wrong answers. What's the best way to attack this problem?