## Solving the Equation (a - 4)(a + 3) = 8

This equation involves a quadratic expression and we need to solve for the unknown variable 'a'. Let's break down the steps to find the solution.

### 1. Expand the Equation

First, expand the left side of the equation by multiplying the two factors:

(a - 4)(a + 3) = a² - a - 12

Now, the equation becomes:

a² - a - 12 = 8

### 2. Move Constant Term to the Left Side

To make it easier to solve, move the constant term (8) to the left side of the equation:

a² - a - 12 - 8 = 0

This simplifies to:

a² - a - 20 = 0

### 3. Factor the Quadratic Expression

Now we need to factor the quadratic expression on the left side:

(a - 5)(a + 4) = 0

### 4. Solve for 'a'

For the product of two factors to be zero, at least one of the factors must be zero. So, we have two possible solutions:

**a - 5 = 0**which leads to**a = 5****a + 4 = 0**which leads to**a = -4**

### Conclusion

Therefore, the solutions to the equation (a - 4)(a + 3) = 8 are **a = 5** and **a = -4**.