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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2+2x-1x-2)), so:

(+x^2+2x-1x-2)

We get rid of parentheses

x^2+2x-1x-2

We add all the numbers together, and all the variables

x^2+x-2

Back to the equation:

-(x^2+x-2)


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x^2-x^2-2x-x+2=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
$