To solve the quadratic equation \(x^2 + 3x = 0\) by factoring, follow these steps:

1. **Rewrite the equation:** The given equation is already in the form \(ax^2 + bx + c = 0\):
   \[
   x^2 + 3x = 0
   \]

2. **Factor out the common term:** Notice that both terms on the left side have a common factor of \(x\). Factor out \(x\) from the equation:
   \[
   x(x + 3) = 0
   \]

3. **Apply the Zero Product Property:** According to this property, if the product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for \(x\):
   \[
   x = 0 \quad \text{or} \quad x + 3 = 0
   \]

4. **Solve for \(x\):**
   \[
   x = 0 \quad \text{or} \quad x = -3
   \]

So, the solutions to the equation \(x^2 + 3x = 0\) are \(x = 0\) and \(x = -3\).

Would you like more details or have any questions?

Here are some related questions to further explore this topic:

1. What is the Zero Product Property, and how is it used in solving quadratic equations?
2. How can you determine if a quadratic equation can be factored easily?
3. What are other methods to solve quadratic equations besides factoring?
4. How do you complete the square for a quadratic equation?
5. How is the quadratic formula derived, and how is it used to solve equations?
6. What are the different types of solutions a quadratic equation can have?
7. How do you graph a quadratic equation and identify its roots from the graph?
8. Can all quadratic equations be solved by factoring? Why or why not?

**Tip:** When factoring quadratic equations, always look for a common factor first. This can simplify the equation and make the factoring process easier.

Learn how to solve the quadratic equation x² + 3x = 0 by factoring with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation formula and the application of the Zero Product Property. Suitable for students in Grades 7-9.

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