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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3z^2+9z+z-3)=0

We get rid of parentheses

-3z^2+9z+z-3=0

We add all the numbers together, and all the variables

-3z^2+10z-3=0

a = -3; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-3)·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*-3}=\frac{-18}{-6}
=+3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*-3}=\frac{-2}{-6}
=1/3
$