(5z+8)(4-z)=0

Solution for (5z+8)(4-z)=0 equation:

(5z+8)(4-z)=0

We add all the numbers together, and all the variables

(5z+8)(-1z+4)=0

We multiply parentheses ..

(-5z^2+20z-8z+32)=0

We get rid of parentheses

-5z^2+20z-8z+32=0

We add all the numbers together, and all the variables

-5z^2+12z+32=0

a = -5; b = 12; c = +32;
Δ = b2-4ac
Δ = 122-4·(-5)·32
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-28}{2*-5}=\frac{-40}{-10}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+28}{2*-5}=\frac{16}{-10}
=-1+3/5
$