(3x-6)(3x-1)=(3x-1)(2x-4)

Solution for (3x-6)(3x-1)=(3x-1)(2x-4) equation:

(3x-6)(3x-1)=(3x-1)(2x-4)

We move all terms to the left:

(3x-6)(3x-1)-((3x-1)(2x-4))=0

We multiply parentheses ..

(+9x^2-3x-18x+6)-((3x-1)(2x-4))=0


We calculate terms in parentheses: -((3x-1)(2x-4)), so:

(3x-1)(2x-4)

We multiply parentheses ..

(+6x^2-12x-2x+4)

We get rid of parentheses

6x^2-12x-2x+4

We add all the numbers together, and all the variables

6x^2-14x+4

Back to the equation:

-(6x^2-14x+4)


We get rid of parentheses

9x^2-6x^2-3x-18x+14x+6-4=0

We add all the numbers together, and all the variables

3x^2-7x+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$