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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4z^2+23z+28=0

a = 4; b = 23; c = +28;
Δ = b2-4ac
Δ = 232-4·4·28
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-9}{2*4}=\frac{-32}{8}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+9}{2*4}=\frac{-14}{8}
=-1+3/4
$