(z-1)(z-3)=0

Solution for (z-1)(z-3)=0 equation:

(z-1)(z-3)=0

We multiply parentheses ..

(+z^2-3z-1z+3)=0

We get rid of parentheses

z^2-3z-1z+3=0

We add all the numbers together, and all the variables

z^2-4z+3=0

a = 1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*1}=\frac{2}{2}
=1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*1}=\frac{6}{2}
=3
$