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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2+2x-3x-6)), so:

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

We get rid of parentheses

x^2+2x-3x-6

We add all the numbers together, and all the variables

x^2-1x-6

Back to the equation:

-(x^2-1x-6)


We add all the numbers together, and all the variables

2x-(x^2-1x-6)-2=0

We get rid of parentheses

-x^2+2x+1x+6-2=0

We add all the numbers together, and all the variables

-1x^2+3x+4=0

a = -1; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-1}=\frac{2}{-2}
=-1
$