## Solving the Equation (x+2)(x-8)(x+5) = 0

This equation represents a cubic polynomial. To solve for the values of *x* that satisfy the equation, we can utilize the **Zero Product Property**:

**Zero Product Property:** If the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Applying this to our equation:

**(x+2)(x-8)(x+5) = 0**

This means that one or more of the following must be true:

**x + 2 = 0****x - 8 = 0****x + 5 = 0**

Solving each of these linear equations, we get:

**x = -2****x = 8****x = -5**

Therefore, the solutions to the equation **(x+2)(x-8)(x+5) = 0** are **x = -2, x = 8, and x = -5**.

### Understanding the Concept

This equation represents a cubic function, which is a function with a highest power of 3. The solutions we found are the **roots** or **x-intercepts** of this function. These are the points where the graph of the function crosses the x-axis.

In other words, the solutions to the equation are the values of *x* where the function equals zero.