## Solving the Equation (x+2)(x+3) = (x+1)(x+5)

This equation involves expanding brackets and solving for the unknown variable 'x'. Let's break down the steps:

### Expanding the Brackets

First, we expand both sides of the equation using the distributive property (or FOIL method):

**Left side:**(x+2)(x+3) = x(x+3) + 2(x+3) = x² + 3x + 2x + 6 =**x² + 5x + 6****Right side:**(x+1)(x+5) = x(x+5) + 1(x+5) = x² + 5x + x + 5 =**x² + 6x + 5**

Now our equation looks like this: **x² + 5x + 6 = x² + 6x + 5**

### Simplifying the Equation

Notice that both sides have the term 'x²'. We can subtract 'x²' from both sides to eliminate it:

**x² + 5x + 6 - x² = x² + 6x + 5 - x²**- This simplifies to
**5x + 6 = 6x + 5**

### Isolating 'x'

Now we need to isolate 'x' on one side of the equation. Let's subtract '5x' from both sides:

**5x + 6 - 5x = 6x + 5 - 5x**- This simplifies to
**6 = x + 5**

Finally, subtract '5' from both sides to get 'x' by itself:

**6 - 5 = x + 5 - 5**- This gives us
**x = 1**

### Solution

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