(4+z)(3z+8)=0

Solution for (4+z)(3z+8)=0 equation:

(4+z)(3z+8)=0

We add all the numbers together, and all the variables

(z+4)(3z+8)=0

We multiply parentheses ..

(+3z^2+8z+12z+32)=0

We get rid of parentheses

3z^2+8z+12z+32=0

We add all the numbers together, and all the variables

3z^2+20z+32=0

a = 3; b = 20; c = +32;
Δ = b2-4ac
Δ = 202-4·3·32
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4}{2*3}=\frac{-24}{6}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4}{2*3}=\frac{-16}{6}
=-2+2/3
$