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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

-3(+x^2-2x+x-2)-4x+4=0

We multiply parentheses

-3x^2+6x-3x-4x+6+4=0

We add all the numbers together, and all the variables

-3x^2-1x+10=0

a = -3; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-3)·10
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-3}=\frac{12}{-6}
=-2
$