(X+2)(x+3)-(x-3)(x-2)-2x(x+1)=0

Solution for (X+2)(x+3)-(x-3)(x-2)-2x(x+1)=0 equation:

(X+2)(X+3)-(X-3)(X-2)-2X(X+1)=0

We multiply parentheses

-2X^2+(X+2)(X+3)-(X-3)(X-2)-2X=0

We multiply parentheses ..

-2X^2+(+X^2+3X+2X+6)-(X-3)(X-2)-2X=0

We add all the numbers together, and all the variables

-2X^2+(+X^2+3X+2X+6)-2X-(X-3)(X-2)=0

We get rid of parentheses

-2X^2+X^2+3X+2X-2X-(X-3)(X-2)+6=0

We multiply parentheses ..

-2X^2+X^2-(+X^2-2X-3X+6)+3X+2X-2X+6=0

We add all the numbers together, and all the variables

-1X^2-(+X^2-2X-3X+6)+3X+6=0

We get rid of parentheses

-1X^2-X^2+2X+3X+3X-6+6=0

We add all the numbers together, and all the variables

-2X^2+8X=0

a = -2; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-2}=\frac{-16}{-4}
=+4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-2}=\frac{0}{-4}
=0
$