1. **State the problem:** We need to solve the equation $0 = 0$ for $x$. 2. **Analyze the equation:** The equation $0 = 0$ is an identity, meaning it is true for all values of $x$. 3. **Conclusion:** Since the equation holds for any $x$, the solution set is all real numbers. **Final answer:** $x \in \mathbb{R}$ (all real numbers).