(5n+10)(4n+12)=0

Solution for (5n+10)(4n+12)=0 equation:

(5n+10)(4n+12)=0

We multiply parentheses ..

(+20n^2+60n+40n+120)=0

We get rid of parentheses

20n^2+60n+40n+120=0

We add all the numbers together, and all the variables

20n^2+100n+120=0

a = 20; b = 100; c = +120;
Δ = b2-4ac
Δ = 1002-4·20·120
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20}{2*20}=\frac{-120}{40}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20}{2*20}=\frac{-80}{40}
=-2
$