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

This article will guide you through the process of solving the equation **(x+2)(x+3)-(x-2)(x+5)=6**. We will use algebraic manipulation to isolate the variable 'x' and find its value(s).

### Step 1: Expanding the equation

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

**(x+2)(x+3)**= x² + 3x + 2x + 6 = x² + 5x + 6**(x-2)(x+5)**= x² + 5x - 2x - 10 = x² + 3x - 10

Now, our equation becomes:

**(x² + 5x + 6) - (x² + 3x - 10) = 6**

### Step 2: Simplifying the equation

Next, we simplify the equation by combining like terms:

**x² + 5x + 6 - x² - 3x + 10 = 6****2x + 16 = 6**

### Step 3: Isolating the variable 'x'

To isolate the 'x' term, we subtract 16 from both sides:

**2x + 16 - 16 = 6 - 16****2x = -10**

### Step 4: Solving for 'x'

Finally, we divide both sides by 2 to solve for 'x':

**2x / 2 = -10 / 2****x = -5**

### Conclusion

Therefore, the solution to the equation **(x+2)(x+3)-(x-2)(x+5)=6** is **x = -5**.