The problem presented is to solve the quadratic equation $x^2 - 2x = 0$ by factoring.

Solution:

1. Factorize the equation: The equation is $x^2 - 2x = 0$. To factorize: $x(x - 2) = 0$

2. Solve for $x$: Using the zero product property, set each factor equal to 0: $x = 0 \quad \text{or} \quad x - 2 = 0$ Solve the second equation: $x = 2$

3. Solutions: The solutions to the equation are: $x = 0 \quad \text{and} \quad x = 2$

Let me know if you'd like a deeper explanation or more examples.

Here are some related questions for further practice:

1. How do you solve quadratic equations that can't be factored easily?
2. Can this equation be solved by completing the square? If so, how?
3. What is the graph of $y = x^2 - 2x$, and how do the solutions relate to its x-intercepts?
4. How does the discriminant of a quadratic equation help determine the number of solutions?
5. What is the difference between solving by factoring and solving using the quadratic formula?

Tip: Always check if a quadratic equation can be factored easily before using other methods like completing the square or the quadratic formula.