## Solving the Equation: (x+1)(x+5) = (x+3)(x-4) + 3

This article will guide you through the steps of solving the given equation: **(x+1)(x+5) = (x+3)(x-4) + 3**. We will use algebraic manipulation to isolate the variable *x*.

### Step 1: Expanding both sides

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

**Left side:**(x+1)(x+5) = x² + 6x + 5**Right side:**(x+3)(x-4) + 3 = x² - x - 12 + 3 = x² - x - 9

Now, our equation becomes: **x² + 6x + 5 = x² - x - 9**

### Step 2: Simplifying the equation

Notice that we have x² on both sides of the equation. Subtracting x² from both sides cancels it out:

**6x + 5 = -x - 9**

### Step 3: Combining x terms

To get all x terms on one side, add *x* to both sides:

**7x + 5 = -9**

### Step 4: Isolating the x term

Subtract 5 from both sides:

**7x = -14**

### Step 5: Solving for x

Finally, divide both sides by 7:

**x = -2**

### Conclusion

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