5(n+7)(n+6)=0

Solution for 5(n+7)(n+6)=0 equation:

5(n+7)(n+6)=0

We multiply parentheses ..

5(+n^2+6n+7n+42)=0

We multiply parentheses

5n^2+30n+35n+210=0

We add all the numbers together, and all the variables

5n^2+65n+210=0

a = 5; b = 65; c = +210;
Δ = b2-4ac
Δ = 652-4·5·210
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5}{2*5}=\frac{-70}{10}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5}{2*5}=\frac{-60}{10}
=-6
$