Question: Solve the following equation by factoring.
$x^2 - 7x = 0$
1. **State the problem:** Solve the equation $$x^2 - 7x = 0$$ by factoring.
2. **Write the equation:** $$x^2 - 7x = 0$$
3. **Factor the left side:** Factor out the common factor $x$:
$$x(x - 7) = 0$$
4. **Apply the zero product property:** If a product of two factors is zero, then at least one of the factors must be zero:
$$x = 0 \quad \text{or} \quad x - 7 = 0$$
5. **Solve each equation:**
- For $$x = 0$$, the solution is $$x = 0$$.
- For $$x - 7 = 0$$, add 7 to both sides:
$$x = 7$$
6. **Write the solution set:**
$$\{0, 7\}$$
**Final answer:** The solution set is $$\{0, 7\}$$.