(2z+7)(4+z)=0

Solution for (2z+7)(4+z)=0 equation:

(2z+7)(4+z)=0

We add all the numbers together, and all the variables

(2z+7)(z+4)=0

We multiply parentheses ..

(+2z^2+8z+7z+28)=0

We get rid of parentheses

2z^2+8z+7z+28=0

We add all the numbers together, and all the variables

2z^2+15z+28=0

a = 2; b = 15; c = +28;
Δ = b2-4ac
Δ = 152-4·2·28
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-1}{2*2}=\frac{-16}{4}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+1}{2*2}=\frac{-14}{4}
=-3+1/2
$