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

This article will guide you through the steps to solve the given equation: (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0.

### 1. Expanding the Equation

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

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

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

**x² + 5x + 6 + x² - 5x + 6 - 2x² - 2x = 0**

### 2. Simplifying the Equation

Combine like terms to simplify the equation:

**(-2x² + x² + x²) + (5x - 5x - 2x) + (6 + 6) = 0**

**-2x + 12 = 0**

### 3. Isolating the Variable

Next, isolate the variable term by subtracting 12 from both sides:

**-2x = -12**

### 4. Solving for x

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

**x = 6**

### Conclusion

Therefore, the solution to the equation (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0 is **x = 6**.