-3(z-8)(-z+9)=0

Solution for -3(z-8)(-z+9)=0 equation:

-3(z-8)(-z+9)=0

We add all the numbers together, and all the variables

-3(z-8)(-1z+9)=0

We multiply parentheses ..

-3(-1z^2+9z+8z-72)=0

We multiply parentheses

3z^2-27z-24z+216=0

We add all the numbers together, and all the variables

3z^2-51z+216=0

a = 3; b = -51; c = +216;
Δ = b2-4ac
Δ = -512-4·3·216
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{-(-51)-3}{2*3}=\frac{48}{6}
=8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3}{2*3}=\frac{54}{6}
=9
$