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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+6x^2+2x-6x-2))+((-4x)-6)(2x-2)=0


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

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

We get rid of parentheses

6x^2+2x-6x-2

We add all the numbers together, and all the variables

6x^2-4x-2

Back to the equation:

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



We calculate terms in parentheses: +((-4x)-6)(2x-2), so:

(-4x)-6)(2x-2

We get rid of parentheses

-4x-6)(2x-2

Back to the equation:

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


We get rid of parentheses

-6x^2+4x+(-4x-6)(2x-2)+2=0

We multiply parentheses ..

-6x^2+(-8x^2+8x-12x+12)+4x+2=0

We get rid of parentheses

-6x^2-8x^2+8x-12x+4x+12+2=0

We add all the numbers together, and all the variables

-14x^2+14=0

a = -14; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-14)·14
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*-14}=\frac{-28}{-28}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*-14}=\frac{28}{-28}
=-1
$