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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-4z^2-7z+16z+28)=0

We get rid of parentheses

-4z^2-7z+16z+28=0

We add all the numbers together, and all the variables

-4z^2+9z+28=0

a = -4; b = 9; c = +28;
Δ = b2-4ac
Δ = 92-4·(-4)·28
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-23}{2*-4}=\frac{-32}{-8}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+23}{2*-4}=\frac{14}{-8}
=-1+3/4
$