Expanding the left side of the equation, we get:

X(X-3) - (X+2)(X+1)
= X^2 - 3X - (X^2 + 3X + 2)
= X^2 - 3X - X^2 - 3X - 2
= -6X - 2

Now, we have the equation:

-6X - 2 = 10

Adding 2 to both sides:

-6X = 12

Dividing by -6:

X = -2

Therefore, the solution to the equation X(X-3)-(x+2)(X+1) = 10 is X = -2.