## Solving the Equation: (x+3)(x+6)-(x+4)(x+5)=2

This article will guide you through the process of solving the equation **(x+3)(x+6)-(x+4)(x+5)=2**.

### Expanding the Equation

First, we need to expand the equation by multiplying out the brackets:

**(x+3)(x+6) = x² + 9x + 18****(x+4)(x+5) = x² + 9x + 20**

Now, substitute these expanded terms back into the original equation:

**(x² + 9x + 18) - (x² + 9x + 20) = 2**

### Simplifying the Equation

Next, simplify the equation by combining like terms:

**x² - x² = 0****9x - 9x = 0****18 - 20 = -2**

This leaves us with: **-2 = 2**

### The Solution

The equation **-2 = 2** is a contradiction. This means there is **no solution** to the original equation **(x+3)(x+6)-(x+4)(x+5)=2**.

**Therefore, the equation has no solution.**