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

This equation presents a simple quadratic equation with a unique solution. Here's how to solve it:

### Expanding the Equation

First, we need to expand both sides of the equation using the distributive property (also known as FOIL):

**Left Side:**(x+1)(x+2) = x² + 2x + x + 2 = x² + 3x + 2**Right Side:**(x-2)(x+2) = x² + 2x - 2x - 4 = x² - 4

Now our equation looks like this:
**x² + 3x + 2 = x² - 4**

### Simplifying and Solving

We can simplify this further by subtracting x² from both sides:

**3x + 2 = -4**

Next, subtract 2 from both sides:

**3x = -6**

Finally, divide both sides by 3:

**x = -2**

### Solution

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

### Checking the Solution

We can check our answer by plugging x = -2 back into the original equation:

**Left Side:**(-2 + 1)(-2 + 2) = (-1)(0) = 0**Right Side:**(-2 - 2)(-2 + 2) = (-4)(0) = 0

Since both sides equal 0, our solution is correct.