## Solving the Equation: (x+2)(x+3)-(x-2)(x+5)=0

This article will guide you through the steps of solving the equation (x+2)(x+3)-(x-2)(x+5)=0. We will utilize the distributive property and simplification techniques to find the solution for *x*.

### 1. Expand the Products:

First, we need to expand the products using the distributive property (also known as FOIL method):

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

Now, substitute these expanded terms back into the original equation:

x² + 5x + 6 - (x² + 3x - 10) = 0

### 2. Simplify the Equation:

Next, we can simplify the equation by distributing the negative sign and combining like terms:

x² + 5x + 6 - x² - 3x + 10 = 0 2x + 16 = 0

### 3. Isolate the Variable:

To isolate the variable *x*, subtract 16 from both sides of the equation:

2x = -16

### 4. Solve for x:

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

x = -8

### Solution:

Therefore, the solution to the equation (x+2)(x+3)-(x-2)(x+5)=0 is **x = -8**.