## Solving the Equation: (x+3)(x+4) = (x+1)(x+2)

This equation presents a simple quadratic equation that can be solved using a few algebraic steps. Let's break down the process:

### Expanding the Equation

First, we need to expand both sides of the equation using the FOIL (First, Outer, Inner, Last) method:

**Left Side:**(x+3)(x+4) = x² + 4x + 3x + 12 = x² + 7x + 12**Right Side:**(x+1)(x+2) = x² + 2x + x + 2 = x² + 3x + 2

Now our equation looks like this: **x² + 7x + 12 = x² + 3x + 2**

### Simplifying the Equation

Next, we need to simplify the equation by combining like terms and bringing all terms to one side:

- Subtract
**x²**from both sides: 7x + 12 = 3x + 2 - Subtract
**3x**from both sides: 4x + 12 = 2 - Subtract
**12**from both sides: 4x = -10

### Solving for x

Finally, we can solve for **x** by dividing both sides by **4**:

**x = -10/4 = -5/2**

### Conclusion

Therefore, the solution to the equation **(x+3)(x+4) = (x+1)(x+2)** is **x = -5/2**.