## Solving the Equation: (x+2)(x+3)-(x-2)(x-5)=-4

This article will walk you through the process of solving the equation **(x+2)(x+3)-(x-2)(x-5)=-4**.

### Expanding the Equation

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

**(x+2)(x+3):**This expands to**x² + 5x + 6**using the FOIL method (First, Outer, Inner, Last).**(x-2)(x-5):**This expands to**x² - 7x + 10**using the FOIL method.

Now, our equation becomes: **x² + 5x + 6 - (x² - 7x + 10) = -4**

### Simplifying the Equation

Next, we can simplify the equation by distributing the negative sign:

**x² + 5x + 6 - x² + 7x - 10 = -4**

Combining like terms, we get: **12x - 4 = -4**

### Isolating the Variable

Now, let's isolate the variable **x** by adding **4** to both sides:

**12x = 0**

### Solving for x

Finally, divide both sides by **12** to solve for **x**:

**x = 0**

### Conclusion

Therefore, the solution to the equation **(x+2)(x+3)-(x-2)(x-5)=-4** is **x = 0**.