## Solving the Equation: (x+1)(x+9) = (x+3)(x+5)

This equation involves expanding both sides and then solving for *x*. Let's break down the steps:

### 1. Expand both sides of the equation:

**(x+1)(x+9):**Using the FOIL method (First, Outer, Inner, Last) we get:- x² + 9x + x + 9 = x² + 10x + 9

**(x+3)(x+5):**Similarly, we get:- x² + 5x + 3x + 15 = x² + 8x + 15

Now, our equation becomes:
**x² + 10x + 9 = x² + 8x + 15**

### 2. Simplify the equation:

- Subtract
**x²**from both sides:- 10x + 9 = 8x + 15

- Subtract
**8x**from both sides:- 2x + 9 = 15

- Subtract
**9**from both sides:- 2x = 6

### 3. Solve for x:

- Divide both sides by
**2**:- x = 3

### Solution:

Therefore, the solution to the equation (x+1)(x+9) = (x+3)(x+5) is **x = 3**.