We have the equation:

\[
(x + 4)(x - 8)(2x - 7) = 0
\]

To solve for \(x\), we use the **zero-product property**, which states that if the product of several factors is zero, at least one of the factors must be zero.

### Step 1: Set each factor equal to zero.

1. \(x + 4 = 0\)
2. \(x - 8 = 0\)
3. \(2x - 7 = 0\)

### Step 2: Solve each equation separately.

1. \(x + 4 = 0 \Rightarrow x = -4\)
2. \(x - 8 = 0 \Rightarrow x = 8\)
3. \(2x - 7 = 0 \Rightarrow 2x = 7 \Rightarrow x = \frac{7}{2} \)

### Final Solutions:
The values of \(x\) are:

\[
x = -4, \quad x = 8, \quad x = \frac{7}{2}
\]

Let me know if you'd like more details on any step!

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Here are some related questions to explore:

1. How can the zero-product property be applied to higher-degree polynomials?
2. What if one of the factors was squared, how would that affect the solution?
3. How would you solve the equation if it had more than three factors?
4. Can complex solutions arise when solving polynomial equations using the zero-product property?
5. What is the graphical interpretation of the solutions to this equation?

**Tip:** Always check the equation for common factors before applying the zero-product property.

Learn how to solve the algebraic equation (x+4)(x-8)(2x-7) = 0 by applying the zero-product property. Step-by-step breakdown of solving for x, including factoring and using basic algebraic principles. Suitable for students in Grades 8-10.

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