(5z+8)(5-z)=0

Solution for (5z+8)(5-z)=0 equation:

(5z+8)(5-z)=0

We add all the numbers together, and all the variables

(5z+8)(-1z+5)=0

We multiply parentheses ..

(-5z^2+25z-8z+40)=0

We get rid of parentheses

-5z^2+25z-8z+40=0

We add all the numbers together, and all the variables

-5z^2+17z+40=0

a = -5; b = 17; c = +40;
Δ = b2-4ac
Δ = 172-4·(-5)·40
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-33}{2*-5}=\frac{-50}{-10}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+33}{2*-5}=\frac{16}{-10}
=-1+3/5
$