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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-6x^2+6x+2=0

a = -6; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-6)·2
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-6}=\frac{-6-2\sqrt{21}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-6}=\frac{-6+2\sqrt{21}}{-12}
$