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To solve this problem, we need to factor and solve the given quadratic equation using the distributive property.

### Step 1: The given equation is:
\[ 3x^2 + 24x = 0 \]

### Step 2: Factor the equation using the distributive property.
Factor out the greatest common factor (GCF), which is \( 3x \):
\[
3x(x + 8) = 0
\]

So the factored form is:
\[
3x(x + 8) = 0
\]

### Step 3: Solve the factored equation.
We can set each factor equal to zero:

1. \( 3x = 0 \) → \( x = 0 \)
2. \( x + 8 = 0 \) → \( x = -8 \)

### Solution:
The solutions to the equation are:
\[
x = 0 \quad \text{and} \quad x = -8
\]

Thus, the factored form is \( 3x(x + 8) \), and the solutions are \( x = 0 \) and \( x = -8 \).

Do you want more details on any part of the solution or have any questions? Here are five related questions you might find helpful:

1. What is the distributive property and how is it used in factoring?
2. How do you determine the greatest common factor (GCF) in an expression?
3. What other methods can be used to factor quadratic equations?
4. How can you verify if the solutions are correct?
5. What is the significance of having two solutions for a quadratic equation?

### Tip:
When solving quadratic equations, always check if you can factor out a GCF first to simplify the process.

Using the Distributive Property to factorize the equation 3x^2 + 24x = 0.

Learn how to factorize the quadratic equation 3x^2 + 24x = 0 using the distributive property. This solution demonstrates factoring out the greatest common factor (GCF) and applying the zero product property to find the solutions x = 0 and x = -8. Suitable for Grades 7-9.

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