4x2-4x+1=(2x-1)(x-2)

Solution for 4x2-4x+1=(2x-1)(x-2) equation:

4x^2-4x+1=(2x-1)(x-2)

We move all terms to the left:

4x^2-4x+1-((2x-1)(x-2))=0

We multiply parentheses ..

4x^2-((+2x^2-4x-1x+2))-4x+1=0


We calculate terms in parentheses: -((+2x^2-4x-1x+2)), so:

(+2x^2-4x-1x+2)

We get rid of parentheses

2x^2-4x-1x+2

We add all the numbers together, and all the variables

2x^2-5x+2

Back to the equation:

-(2x^2-5x+2)


We add all the numbers together, and all the variables

4x^2-4x-(2x^2-5x+2)+1=0

We get rid of parentheses

4x^2-2x^2-4x+5x-2+1=0

We add all the numbers together, and all the variables

2x^2+x-1=0

a = 2; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·2·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*2}=\frac{2}{4}
=1/2
$