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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

z^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
$