(3x+1)(-9x-6)=0

Solution for (3x+1)(-9x-6)=0 equation:

(3x+1)(-9x-6)=0

We multiply parentheses ..

(-27x^2-18x-9x-6)=0

We get rid of parentheses

-27x^2-18x-9x-6=0

We add all the numbers together, and all the variables

-27x^2-27x-6=0

a = -27; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·(-27)·(-6)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9}{2*-27}=\frac{18}{-54}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9}{2*-27}=\frac{36}{-54}
=-2/3
$