## Factoring and Solving the Expression (x+4)(x-7) + 3(x-7)

This expression can be simplified and factored by recognizing a common factor.

**1. Identify the Common Factor:**

Observe that both terms in the expression share a common factor of **(x - 7)**.

**2. Factor out the Common Factor:**

- Rewrite the expression by factoring out (x - 7): (x - 7) [(x + 4) + 3]

**3. Simplify the Expression:**

- Combine the terms inside the brackets: (x - 7) (x + 7)

**4. Final Factored Form:**

- The simplified and factored form of the expression is:
**(x - 7)(x + 7)**

**Solving for x:**

To find the values of x that make the expression equal to zero, we can use the **Zero Product Property**: If the product of two factors is zero, then at least one of the factors must be zero.

- Set each factor equal to zero and solve for x:
- x - 7 = 0 => x = 7
- x + 7 = 0 => x = -7

**Therefore, the solutions to the equation (x + 4)(x - 7) + 3(x - 7) = 0 are x = 7 and x = -7.**