Possible even integer values of $y$ under a system of quadratic and linear equations

Question

If $$25(9x^2+y^2)+9z^2-15(5xy+yz+3zx)=0$$ and $$x+y+z=18$$ then possible even integral values of ($y$) less than $15$ are: ?

My attempt: I manipulated the given equation in this form $$(15x)^2+(5y)^2+(3z)^2-(15x)(5y)-(5y)(3z)-(15x)(3z)$$ which is of the form $$a^2+b^2+c^2-ab-bc-ca$$ but what should I do after this? Any hints?

Answer 1

$$2(a^2+b^2+c^2-ab-bc-ca)=\sum(a-b)^2$$

Now for real $x, x^2\ge0$

So what if $a-b,b-c,c-a$ are real?