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

Solution for 4(z+3)(-z+8)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

4(-1z^2+8z-3z+24)=0

We multiply parentheses

-4z^2+32z-12z+96=0

We add all the numbers together, and all the variables

-4z^2+20z+96=0

a = -4; b = 20; c = +96;
Δ = b2-4ac
Δ = 202-4·(-4)·96
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-44}{2*-4}=\frac{-64}{-8}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+44}{2*-4}=\frac{24}{-8}
=-3
$