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

This equation involves a product of three factors that equals zero. To find the solutions, we can use the **Zero Product Property**. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Let's apply this to our equation:

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

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

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

Now, we can solve each of these simple equations:

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

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

## Understanding the Solutions

These solutions represent the **x-intercepts** of the graph of the function y = (x+5)(x+2)(x-8). This means that the graph crosses the x-axis at the points (-5, 0), (-2, 0), and (8, 0).

## Conclusion

By applying the Zero Product Property, we have successfully solved the equation (x+5)(x+2)(x-8) = 0. We found three distinct solutions, which represent the x-intercepts of the corresponding function. This method can be applied to solve similar equations involving products of factors.