And this is the final iteration of the equation before I solve the system of equations:

0x[sup]6[/sup] + 0x[sup]5[/sup] + 0x[sup]4[/sup] + 0x[sup]3[/sup] + 2x[sup]2[/sup] + 7x + 0 = (3A + 3E + G)x[sup]6[/sup] + (-A + 3B + 2E + 3F + 2G)x[sup]5[/sup] + (35A - B + 3C + 37E + 2F + 21G)x[sup]4[/sup] + (-34A + 35B - 4C + 3D + 18E + 37F + 26G)x[sup]3[/sup] + (102A - 34B + 18C - 4D + 91E - 18F + 139G)x[sup]2[/sup] + (-168A + 102B - 24C + 18D - 196E + 91F + 84G)x - 168B - 24D - 196F + 294G

Now I do the whole coefficient system of equations thing.