The teacher will be very surprised to see your correct solution 😉
2 2 2 3*z + 7*y + 8*x - 8*y*z + 4*x*z + 12*x*y = 0
8*x^2 + 12*x*y + 4*x*z + 7*y^2 - 8*y*z + 3*z^2 = 0