(5z+7)(4-z)=0

Solution for (5z+7)(4-z)=0 equation:

(5z+7)(4-z)=0

We add all the numbers together, and all the variables

(5z+7)(-1z+4)=0

We multiply parentheses ..

(-5z^2+20z-7z+28)=0

We get rid of parentheses

-5z^2+20z-7z+28=0

We add all the numbers together, and all the variables

-5z^2+13z+28=0

a = -5; b = 13; c = +28;
Δ = b2-4ac
Δ = 132-4·(-5)·28
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-27}{2*-5}=\frac{-40}{-10}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+27}{2*-5}=\frac{14}{-10}
=-1+2/5
$