The teacher will be very surprised to see your correct solution 😉
2 2 2 y + 16*z + 36*x + 8*y*z + 48*x*z + 120*x*y = 0
36*x^2 + 120*x*y + 48*x*z + y^2 + 8*y*z + 16*z^2 = 0