(2-2x)(6-2x)=(2-2x)(9x+1)

Solution for (2-2x)(6-2x)=(2-2x)(9x+1) equation:

(2-2x)(6-2x)=(2-2x)(9x+1)

We move all terms to the left:

(2-2x)(6-2x)-((2-2x)(9x+1))=0

We add all the numbers together, and all the variables

(-2x+2)(-2x+6)-((-2x+2)(9x+1))=0

We multiply parentheses ..

(+4x^2-12x-4x+12)-((-2x+2)(9x+1))=0


We calculate terms in parentheses: -((-2x+2)(9x+1)), so:

(-2x+2)(9x+1)

We multiply parentheses ..

(-18x^2-2x+18x+2)

We get rid of parentheses

-18x^2-2x+18x+2

We add all the numbers together, and all the variables

-18x^2+16x+2

Back to the equation:

-(-18x^2+16x+2)


We get rid of parentheses

4x^2+18x^2-12x-4x-16x+12-2=0

We add all the numbers together, and all the variables

22x^2-32x+10=0

a = 22; b = -32; c = +10;
Δ = b2-4ac
Δ = -322-4·22·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12}{2*22}=\frac{20}{44}
=5/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12}{2*22}=\frac{44}{44}
=1
$