(2m-3)(3m+2)=0

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

(2m-3)(3m+2)=0

We multiply parentheses ..

(+6m^2+4m-9m-6)=0

We get rid of parentheses

6m^2+4m-9m-6=0

We add all the numbers together, and all the variables

6m^2-5m-6=0

a = 6; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·6·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*6}=\frac{-8}{12}
=-2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*6}=\frac{18}{12}
=1+1/2
$