3 Variables, One Equation

Question

What triples (x, y, z) will satisfy the following equation?:

$x^2$ + $y^2$ + $z^2$ = $7(x+y+z)$

I tried factoring the left side as $(x+y+z)^2 - 2xyz$, and I wasn't sure how to continue from there.

EDIT: x, y, and z are positive integers.

Answer 1

Instead of the factoring you do, it might help instead to group terms and rewrite to be in the form $(x-7/2)^2 + (y-7/2)^2 + (z-7/2)^2 = c$, which is now asking for integer points on some sphere.