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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+6x^2+18x-2x-6)+6=0

We get rid of parentheses

6x^2+18x-2x-6+6=0

We add all the numbers together, and all the variables

6x^2+16x=0

a = 6; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·6·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*6}=\frac{0}{12}
=0
$