The equation you've provided is:

$3x + 3y + 3z = 3xyz$

We can simplify the equation by dividing through by 3:

$x + y + z = xyz$

This is a symmetric equation, meaning that $x$, $y$, and $z$ are interchangeable. It's a non-linear equation and doesn't have a simple solution without additional constraints or conditions. However, it can be approached in several ways, such as looking for integer solutions or solving using specific methods like substitution or factorization.

One possible approach is trial and error with small integer values, or you could use a systematic approach to explore potential solutions.

Some possible integer solutions:

• If $x = y = z = 1$, then:

$1 + 1 + 1 = 1 \cdot 1 \cdot 1$

which is true. So, $x = y = z = 1$ is a solution.

Would you like to explore more solutions or solve this equation under specific conditions? Let me know if you'd like further details or an alternative method of solving.

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Here are five related questions:

1. How can we solve the equation $x + y + z = xyz$ for non-integer values of $x$, $y$, and $z$?
2. Can we find a general form for all possible solutions of this equation?
3. How does the symmetry of the equation $x + y + z = xyz$ help in solving it?
4. What happens if we impose specific conditions on $x$, $y$, or $z$, like $x = y$ or $z = 1$?
5. How can we use numerical methods to approximate solutions to this equation?

Tip: Try starting with specific simple values for $x$, $y$, and $z$ (like 1 or 2) to quickly identify integer solutions before using more advanced techniques.