(4n+6)(8n+8)=0

Solution for (4n+6)(8n+8)=0 equation:

(4n+6)(8n+8)=0

We multiply parentheses ..

(+32n^2+32n+48n+48)=0

We get rid of parentheses

32n^2+32n+48n+48=0

We add all the numbers together, and all the variables

32n^2+80n+48=0

a = 32; b = 80; c = +48;
Δ = b2-4ac
Δ = 802-4·32·48
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-16}{2*32}=\frac{-96}{64}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+16}{2*32}=\frac{-64}{64}
=-1
$