https://file.aiquickdraw.com/mathbot/file/1725531181346djy74m4b.jpg

The equation shown in the image is:

\[
5x(x + 6) = 0
\]

To solve this equation, we'll apply the **Zero Product Property**, which states that if the product of two factors is zero, at least one of the factors must be zero. 

### Step 1: Set each factor equal to zero
We have two factors: \( 5x \) and \( (x + 6) \).

1. \( 5x = 0 \)
2. \( x + 6 = 0 \)

### Step 2: Solve for \( x \)
1. Solve \( 5x = 0 \):
   \[
   x = 0
   \]

2. Solve \( x + 6 = 0 \):
   \[
   x = -6
   \]

### Final Answer:
The solutions to the equation are:
\[
x = 0 \quad \text{or} \quad x = -6
\]

Would you like any additional details or explanations?

Here are 5 related questions to deepen your understanding:

1. How would the solution change if the equation were \( 5x(x + 6) = 10 \)?
2. What is the Zero Product Property, and why is it useful in solving quadratic equations?
3. How can we graph the equation \( 5x(x + 6) = 0 \) to visualize the solutions?
4. If we factor more complicated quadratic equations, what are some common methods?
5. How can we solve quadratic equations that don't factor easily?

**Tip:** Always check your solutions by substituting them back into the original equation to verify they satisfy the equation.

This article demonstrates how to solve the quadratic equation 5x(x + 6) = 0 by applying the Zero Product Property. Learn the step-by-step process of setting each factor equal to zero and solving for x, with final solutions x = 0 or x = -6. Ideal for students in Grades 7-9.

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