(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 get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

-2x^2+(+x^2+3x+2x+6)-5=0

We get rid of parentheses

-2x^2+x^2+3x+2x+6-5=0

We add all the numbers together, and all the variables

-1x^2+5x+1=0

a = -1; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-1)·1
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{29}}{2*-1}=\frac{-5-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{29}}{2*-1}=\frac{-5+\sqrt{29}}{-2}
$