(6-z)(2z-3)=0

Solution for (6-z)(2z-3)=0 equation:

(6-z)(2z-3)=0

We add all the numbers together, and all the variables

(-1z+6)(2z-3)=0

We multiply parentheses ..

(-2z^2+3z+12z-18)=0

We get rid of parentheses

-2z^2+3z+12z-18=0

We add all the numbers together, and all the variables

-2z^2+15z-18=0

a = -2; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·(-2)·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*-2}=\frac{-24}{-4}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-2}=\frac{-6}{-4}
=1+1/2
$