(3x+5)(-2x-3)=0

Solution for (3x+5)(-2x-3)=0 equation:

(3x+5)(-2x-3)=0

We multiply parentheses ..

(-6x^2-9x-10x-15)=0

We get rid of parentheses

-6x^2-9x-10x-15=0

We add all the numbers together, and all the variables

-6x^2-19x-15=0

a = -6; b = -19; c = -15;
Δ = b2-4ac
Δ = -192-4·(-6)·(-15)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-1}{2*-6}=\frac{18}{-12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+1}{2*-6}=\frac{20}{-12}
=-1+2/3
$