(-z-1)(z+7)=0

Solution for (-z-1)(z+7)=0 equation:

(-z-1)(z+7)=0

We add all the numbers together, and all the variables

(-1z-1)(z+7)=0

We multiply parentheses ..

(-1z^2-7z-1z-7)=0

We get rid of parentheses

-1z^2-7z-1z-7=0

We add all the numbers together, and all the variables

-1z^2-8z-7=0

a = -1; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·(-1)·(-7)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*-1}=\frac{2}{-2}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*-1}=\frac{14}{-2}
=-7
$