To solve the equation \((x-2)(x+4) = 0\), we use the **Zero Product Property**. The property states that if the product of two factors is zero, then at least one of the factors must be zero. 

### Steps to Solve

1. **Set each factor equal to zero**:
   \[
   x - 2 = 0 \quad \text{or} \quad x + 4 = 0
   \]

2. **Solve each equation for \(x\)**:

   - For \(x - 2 = 0\):
     \[
     x = 2
     \]

   - For \(x + 4 = 0\):
     \[
     x = -4
     \]

### Solutions

The solutions to the equation \((x-2)(x+4) = 0\) are:
\[
\boxed{x = 2 \text{ and } x = -4}
\]

Would you like more details or have any questions?

Here are some related questions for further practice:

1. Solve the quadratic equation \((x - 5)(x + 3) = 0\).
2. What are the roots of the equation \(x^2 - 4 = 0\)?
3. Solve the equation \((x + 6)(x - 1) = 0\).
4. If \((2x - 3)(x + 7) = 0\), what are the values of \(x\)?
5. How do you solve \((x - a)(x - b) = 0\) in terms of \(a\) and \(b\)?

**Tip:** The Zero Product Property is a powerful tool for solving equations where the product of multiple factors is zero. Remember to apply it whenever you encounter a product set to zero.

Learn how to solve the equation (x-2)(x+4) = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including quadratic equations and the zero product property. Suitable for students in Grades 7-9.

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