## Solving the Quadratic Equation: (x-2)(x+1) = (x-1)(x+3)

This article will guide you through solving the quadratic equation (x-2)(x+1) = (x-1)(x+3). We'll break down the steps and explain the concepts involved.

### 1. Expanding the Equation

First, we need to expand both sides of the equation by applying the distributive property (FOIL method):

**Left side:**(x-2)(x+1) = x² - x - 2**Right side:**(x-1)(x+3) = x² + 2x - 3

Now, our equation becomes: x² - x - 2 = x² + 2x - 3

### 2. Simplifying the Equation

Next, we can simplify the equation by moving all terms to one side:

- Subtract x² from both sides: -x - 2 = 2x - 3
- Subtract 2x from both sides: -3x - 2 = -3
- Add 2 to both sides: -3x = -1

### 3. Solving for x

Finally, we can solve for x by dividing both sides by -3:

- x = -1 / -3
**x = 1/3**

### Conclusion

Therefore, the solution to the quadratic equation (x-2)(x+1) = (x-1)(x+3) is **x = 1/3**.

This equation was relatively simple to solve because it simplified to a linear equation after expanding and simplifying. However, the same principles can be applied to more complex quadratic equations.