Solve :
`(x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0`

Answer

To solve the equation \((x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0\), we will follow these steps:

### Step 1: Expand the expressions
We will expand each of the products in the equation.

1. Expand \((x+2)(x+3)\):
\[ (x+2)(x+3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 \]

2. Expand \((x-3)(x-2)\):
\[ (x-3)(x-2) = x^2 - 2x - 3x + 6 = x^2 - 5x + 6 \]

3. Expand \(-2x(x+1)\):
\[ -2x(x+1) = -2x^2 - 2x \]

Now substitute these expansions back into the equation:
\[ x^2 + 5x + 6 + x^2 - 5x + 6 - 2x^2 - 2x = 0 \]

### Step 2: Combine like terms
Now, let's combine the like terms:
\[ (x^2 + x^2 - 2x^2) + (5x - 5x - 2x) + (6 + 6) = 0 \]
This simplifies to:
\[ 0x^2 - 2x + 12 = 0 \]
or simply:
\[ -2x + 12 = 0 \]

### Step 3: Solve for \(x\)
Now, we will isolate \(x\):
\[ -2x = -12 \]
Dividing both sides by -2:
\[ x = 6 \]

### Final Solution
The solution to the equation \((x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0\) is:
\[ \boxed{6} \]