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

This article will guide you through the steps of solving the quadratic equation (x-3)(x+4)=8.

### 1. Expanding the Equation

First, we need to expand the left side of the equation by multiplying the binomials:

(x-3)(x+4) = x² + x - 12

Now our equation becomes:

x² + x - 12 = 8

### 2. Rearranging the Equation

To solve this quadratic equation, we need to set it equal to zero. Subtract 8 from both sides:

x² + x - 20 = 0

### 3. Factoring the Equation

Now we need to factor the quadratic expression. We are looking for two numbers that add up to 1 (the coefficient of the x term) and multiply to -20 (the constant term). These numbers are 5 and -4.

Therefore, we can factor the equation as:

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

### 4. Solving for x

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

**x + 5 = 0**=> x = -5**x - 4 = 0**=> x = 4

### Conclusion

The solutions to the quadratic equation (x-3)(x+4)=8 are **x = -5** and **x = 4**.