2(6a+4)(2a+3)=0

Solution for 2(6a+4)(2a+3)=0 equation:

2(6a+4)(2a+3)=0

We multiply parentheses ..

2(+12a^2+18a+8a+12)=0

We multiply parentheses

24a^2+36a+16a+24=0

We add all the numbers together, and all the variables

24a^2+52a+24=0

a = 24; b = 52; c = +24;
Δ = b2-4ac
Δ = 522-4·24·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-20}{2*24}=\frac{-72}{48}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+20}{2*24}=\frac{-32}{48}
=-2/3
$