Question: User: $x^2$ - $x$ = 0
1. **State the problem:** Solve the quadratic equation $$x^2 - x = 0$$.
2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the zero product property which states if $$ab=0$$ then either $$a=0$$ or $$b=0$$.
3. **Factor the equation:**
$$x^2 - x = x(x - 1) = 0$$
4. **Apply zero product property:**
$$x = 0 \quad \text{or} \quad x - 1 = 0$$
5. **Solve each equation:**
$$x = 0$$
$$x = 1$$
6. **Final answer:** The solutions to the equation $$x^2 - x = 0$$ are $$x = 0$$ and $$x = 1$$.