We are given the equation:

\[
(2x + 3)(8x - 9) = 0
\]

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

So, set each factor equal to zero:

1. \( 2x + 3 = 0 \)
2. \( 8x - 9 = 0 \)

### Solving for \( x \):

1. \( 2x + 3 = 0 \)
   \[
   2x = -3
   \]
   \[
   x = \frac{-3}{2}
   \]

2. \( 8x - 9 = 0 \)
   \[
   8x = 9
   \]
   \[
   x = \frac{9}{8}
   \]

### Final Answer:

The solutions are:
\[
x = \frac{-3}{2} \quad \text{or} \quad x = \frac{9}{8}
\]

Would you like further details on any of these steps?

Here are 5 related questions to consider:
1. What is the Zero Product Property, and how is it applied in different scenarios?
2. How would the solution change if the factors were more complex expressions?
3. What if there were additional terms on the right-hand side instead of 0? How would the approach change?
4. Can you use factoring to solve equations with higher powers of \(x\)?
5. How would you graph the solutions \(x = -\frac{3}{2}\) and \(x = \frac{9}{8}\)?

**Tip**: Always simplify each factor before solving it, to avoid any errors in the steps.

This guide explains how to solve the algebraic equation (2x + 3)(8x − 9) = 0 using the Zero Product Property. Learn the step-by-step process of factoring and solving for x, covering essential concepts for students in Grades 7-9.

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