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The equation given is:

\[
3(x + 2)(x - 9) = 0
\]

To find the solutions, we use the fact that if the product of two factors is zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero:

1. \( x + 2 = 0 \)
   
   Solving for \( x \), we get:
   \[
   x = -2
   \]

2. \( x - 9 = 0 \)
   
   Solving for \( x \), we get:
   \[
   x = 9
   \]

Thus, the solutions to the equation are \( x = -2 \) and \( x = 9 \).

Looking at the answer choices, the correct answers are:

- \( -2 \)
- \( 9 \)

Would you like further details or explanations?

Here are five questions to expand on the topic:
1. How would the solutions change if the equation were \( 3(x + 2)(x - 9) = 6 \)?
2. What if the expression was expanded and simplified to a quadratic form before solving?
3. What is the significance of the constant "3" in this equation?
4. Can this equation have any non-real or complex solutions?
5. How would you graph this equation to visually identify the solutions?

**Tip:** Always check the factors individually when solving a product of factors equal to zero, as each factor can independently yield a solution.

What are the solutions to 3(x + 2)(x - 9) = 0? Select all that apply.

Learn how to solve the factored equation 3(x + 2)(x - 9) = 0 using the zero-product property. This algebra problem highlights key concepts such as factoring and solving for variables. Ideal for students in Grades 8-10.

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