3(4n+7)(2n+3)=0

Solution for 3(4n+7)(2n+3)=0 equation:

3(4n+7)(2n+3)=0

We multiply parentheses ..

3(+8n^2+12n+14n+21)=0

We multiply parentheses

24n^2+36n+42n+63=0

We add all the numbers together, and all the variables

24n^2+78n+63=0

a = 24; b = 78; c = +63;
Δ = b2-4ac
Δ = 782-4·24·63
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6}{2*24}=\frac{-84}{48}
=-1+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6}{2*24}=\frac{-72}{48}
=-1+1/2
$