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

Solution for 4(z-9)(-z+3)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

4(-1z^2+3z+9z-27)=0

We multiply parentheses

-4z^2+12z+36z-108=0

We add all the numbers together, and all the variables

-4z^2+48z-108=0

a = -4; b = 48; c = -108;
Δ = b2-4ac
Δ = 482-4·(-4)·(-108)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24}{2*-4}=\frac{-72}{-8}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24}{2*-4}=\frac{-24}{-8}
=+3
$