(8+z)(3z+2)=0

Solution for (8+z)(3z+2)=0 equation:

(8+z)(3z+2)=0

We add all the numbers together, and all the variables

(z+8)(3z+2)=0

We multiply parentheses ..

(+3z^2+2z+24z+16)=0

We get rid of parentheses

3z^2+2z+24z+16=0

We add all the numbers together, and all the variables

3z^2+26z+16=0

a = 3; b = 26; c = +16;
Δ = b2-4ac
Δ = 262-4·3·16
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-22}{2*3}=\frac{-48}{6}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+22}{2*3}=\frac{-4}{6}
=-2/3
$