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

Solution for (3x+2)(-6x-3)=0 equation:

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

We multiply parentheses ..

(-18x^2-9x-12x-6)=0

We get rid of parentheses

-18x^2-9x-12x-6=0

We add all the numbers together, and all the variables

-18x^2-21x-6=0

a = -18; b = -21; c = -6;
Δ = b2-4ac
Δ = -212-4·(-18)·(-6)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*-18}=\frac{18}{-36}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*-18}=\frac{24}{-36}
=-2/3
$