(z-6)(z-9)=0

Solution for (z-6)(z-9)=0 equation:

(z-6)(z-9)=0

We multiply parentheses ..

(+z^2-9z-6z+54)=0

We get rid of parentheses

z^2-9z-6z+54=0

We add all the numbers together, and all the variables

z^2-15z+54=0

a = 1; b = -15; c = +54;
Δ = b2-4ac
Δ = -152-4·1·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*1}=\frac{12}{2}
=6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*1}=\frac{18}{2}
=9
$