## Solving the Equation (x^2 - x - 6)(x + 4) = 0

This equation is a **polynomial equation** of degree three. To solve it, 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.

**Step 1: Factor the quadratic expression**

The quadratic expression (x² - x - 6) can be factored as (x - 3)(x + 2).

**Step 2: Apply the Zero Product Property**

Now, the equation becomes:

**(x - 3)(x + 2)(x + 4) = 0**

For this product to be zero, one or more of the factors must be zero. So, we set each factor equal to zero and solve for x:

**x - 3 = 0**=>**x = 3****x + 2 = 0**=>**x = -2****x + 4 = 0**=>**x = -4**

**Therefore, the solutions to the equation (x² - x - 6)(x + 4) = 0 are x = 3, x = -2, and x = -4.**

**In summary:**

- We factored the quadratic expression.
- We applied the Zero Product Property to set each factor equal to zero.
- We solved for x in each equation.

This method provides us with all the solutions to the given equation.