Can anyone please help me to find the generalized equation for $x$,$y$ and $z$? $$
A= P(9+2\cos(x)+2\cos(y)+2\cos(z))
$$
$$
B= P(9+2\cos(x-2\pi/3)+2\cos(y-2\pi/3)+2\cos(z-2\pi/3))
$$
$$
C= P(9+2\cos(x+2\pi/3)+2\cos(y+2\pi/3)+2\cos(z+2\pi/3))
$$

Observation: replacing $A,B,C$ with $A/p$, etc., we have
\begin{align}
A&= (9+2\cos(x)+2\cos(y)+2\cos(z))\\
B&= (9+2\cos(x-2\pi/3)+2\cos(y-2\pi/3)+2\cos(z-2\pi/3))\\
C&= (9+2\cos(x+2\pi/3)+2\cos(y+2\pi/3)+2\cos(z+2\pi/3))
\end{align}
Summing, we get
\begin{align}
A+B+C&= 27 + 2[\cos(x) + \cos(x-2\pi/3) + \cos(x + 2\pi/3] + \ldots \end{align}
where the ellipses denote similar expressions in $y$ and $z$. But this expression in brackets is always zero, so these equations cannot have a solution unless $A + B + C = 27$. 
