(13m+5)(12m-6)=0

Solution for (13m+5)(12m-6)=0 equation:

(13m+5)(12m-6)=0

We multiply parentheses ..

(+156m^2-78m+60m-30)=0

We get rid of parentheses

156m^2-78m+60m-30=0

We add all the numbers together, and all the variables

156m^2-18m-30=0

a = 156; b = -18; c = -30;
Δ = b2-4ac
Δ = -182-4·156·(-30)
Δ = 19044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19044}=138$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-138}{2*156}=\frac{-120}{312}
=-5/13
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+138}{2*156}=\frac{156}{312}
=1/2
$