Question

Help please i need to write 4x^2 -y^2 -8x -4y +16 =0 in standard form.4x^2 -8x - y^2 -4y=-16 so 4(x^2 -2x +1)-(y^2-4y+4= -16 -4 +4 so 4(x-1)^2/-16 -(y-2)^2/-16 =1 so (x-1)^2/-4 -(y-2)^2/-16 so if I multiply everything by -1 it will get rid of my (-) on the left and I'm left with (x-1)^2/4 -(y-2)^2/16= but then I have to multiply the right side to and I'm back to having a -1 My center is (0,2) and its suppose to be (0,-2) can you explain what I'm doing wrong I know it must have something to do with the subtraction sign and negatives??