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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+1

Back to the equation:

-(-1x^2+1)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-4x+1=0

a = 1; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·1·1
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{3}}{2*1}=\frac{4-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{3}}{2*1}=\frac{4+2\sqrt{3}}{2}
$