To solve the quadratic equation:

$x^2 + 8x = 0$

Step 1: Factor the equation.

We can factor out an $x$ from both terms:

$x(x + 8) = 0$

Step 2: Apply the zero product property.

If a product of two factors equals zero, then at least one of the factors must be zero. So, we set each factor equal to zero:

$x = 0 \quad \text{or} \quad x + 8 = 0$

Step 3: Solve each equation.

For $x + 8 = 0$:

$x = -8$

Final Solution:

The solutions are:

$x = 0 \quad \text{or} \quad x = -8$

Would you like more details or have any questions about the solution?

Here are some related questions to help further:

1. How do you solve quadratic equations using the quadratic formula?
2. What is the general form of a quadratic equation?
3. Can you solve quadratic equations by completing the square?
4. What happens if a quadratic equation has complex roots?
5. How do you factor different types of quadratic equations?

Tip: Always check if factoring is possible before using the quadratic formula or completing the square—it can save time!