## Solving the Equation (x+2)(x+3) - (x-1)(x+4) = 0

This article will guide you through the steps of solving the equation **(x+2)(x+3) - (x-1)(x+4) = 0**.

### Expanding the Equation

First, we need to expand the equation by multiplying the factors:

**(x+2)(x+3):**x² + 3x + 2x + 6 = x² + 5x + 6**(x-1)(x+4):**x² + 4x - x - 4 = x² + 3x - 4

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

(x² + 5x + 6) - (x² + 3x - 4) = 0

### Simplifying the Equation

Next, we simplify the equation by removing the parentheses and combining like terms:

x² + 5x + 6 - x² - 3x + 4 = 0 2x + 10 = 0

### Isolating x

To solve for x, we need to isolate it on one side of the equation. Subtract 10 from both sides:

2x = -10

### Solving for x

Finally, divide both sides by 2 to get the value of x:

x = -5

### Conclusion

Therefore, the solution to the equation (x+2)(x+3) - (x-1)(x+4) = 0 is **x = -5**.