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

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

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

We multiply parentheses ..

(+7n^2+49n+6n+42)=0

We get rid of parentheses

7n^2+49n+6n+42=0

We add all the numbers together, and all the variables

7n^2+55n+42=0

a = 7; b = 55; c = +42;
Δ = b2-4ac
Δ = 552-4·7·42
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-43}{2*7}=\frac{-98}{14}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+43}{2*7}=\frac{-12}{14}
=-6/7
$