## Solving the Equation: (x+4)(x+5) = (x+2)(x+6)

This equation involves expanding and simplifying expressions on both sides to find the value of 'x'. Let's break down the steps:

### 1. Expanding the Expressions

We begin by using the distributive property (FOIL method) to expand both sides of the equation:

**Left Side:**(x+4)(x+5) = x² + 5x + 4x + 20 =**x² + 9x + 20****Right Side:**(x+2)(x+6) = x² + 6x + 2x + 12 =**x² + 8x + 12**

Now, our equation looks like this: **x² + 9x + 20 = x² + 8x + 12**

### 2. Simplifying the Equation

Notice that we have x² on both sides. Subtracting x² from both sides will cancel it out:

**(x² + 9x + 20) - x² = (x² + 8x + 12) - x²**

This leaves us with: **9x + 20 = 8x + 12**

### 3. Isolating 'x'

To isolate 'x', we need to move all the terms containing 'x' to one side and constants to the other side. Subtracting 8x from both sides:

**(9x + 20) - 8x = (8x + 12) - 8x**

This gives us: **x + 20 = 12**

Finally, subtracting 20 from both sides:

**(x + 20) - 20 = 12 - 20**

We get: **x = -8**

### Conclusion

Therefore, the solution to the equation (x+4)(x+5) = (x+2)(x+6) is **x = -8**.