x=(x-6)(x-2)

Solution for x=(x-6)(x-2) equation:

x=(x-6)(x-2)

We move all terms to the left:

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

We multiply parentheses ..

-((+x^2-2x-6x+12))+x=0


We calculate terms in parentheses: -((+x^2-2x-6x+12)), so:

(+x^2-2x-6x+12)

We get rid of parentheses

x^2-2x-6x+12

We add all the numbers together, and all the variables

x^2-8x+12

Back to the equation:

-(x^2-8x+12)


We add all the numbers together, and all the variables

x-(x^2-8x+12)=0

We get rid of parentheses

-x^2+x+8x-12=0

We add all the numbers together, and all the variables

-1x^2+9x-12=0

a = -1; b = 9; c = -12;
Δ = b2-4ac
Δ = 92-4·(-1)·(-12)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{33}}{2*-1}=\frac{-9-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*-1}=\frac{-9+\sqrt{33}}{-2}
$