(X-1)(x-1)-(x-1)=0

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

(X-1)(X-1)-(X-1)=0

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-3X+2=0

a = 1; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·1·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-1}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+1}{2*1}=\frac{4}{2}
=2
$