## Solving the Equation: (x+1)(2x+8) = (x+7)(x+3)

This article will guide you through the steps of solving the equation **(x+1)(2x+8) = (x+7)(x+3)**. We will use algebraic manipulation to isolate the variable *x* and find its value(s).

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

First, we need to expand both sides of the equation by multiplying the terms within the parentheses.

**(x+1)(2x+8) = (x+7)(x+3)**

**Left Side:**(x+1)(2x+8) = 2x² + 8x + 2x + 8 = 2x² + 10x + 8**Right Side:**(x+7)(x+3) = x² + 3x + 7x + 21 = x² + 10x + 21

Now, our equation becomes:

**2x² + 10x + 8 = x² + 10x + 21**

### Step 2: Combine like terms

Next, we need to combine like terms on both sides of the equation. In this case, we can subtract x² and 10x from both sides.

**2x² + 10x + 8 - x² - 10x = x² + 10x + 21 - x² - 10x**

This simplifies to:

**x² + 8 = 21**

### Step 3: Isolate the x² term

To isolate the x² term, we can subtract 8 from both sides of the equation.

**x² + 8 - 8 = 21 - 8**

This leaves us with:

**x² = 13**

### Step 4: Solve for x

Finally, to solve for *x*, we need to take the square root of both sides of the equation.

**√x² = ±√13**

Therefore, the solutions to the equation are:

**x = √13** and **x = -√13**

### Conclusion

By carefully following the steps of algebraic manipulation, we successfully solved the equation **(x+1)(2x+8) = (x+7)(x+3)** and found the two solutions: **x = √13** and **x = -√13**.