(12+3z)*(z-17)=0

Solution for (12+3z)*(z-17)=0 equation:

(12+3z)(z-17)=0

We add all the numbers together, and all the variables

(3z+12)(z-17)=0

We multiply parentheses ..

(+3z^2-51z+12z-204)=0

We get rid of parentheses

3z^2-51z+12z-204=0

We add all the numbers together, and all the variables

3z^2-39z-204=0

a = 3; b = -39; c = -204;
Δ = b2-4ac
Δ = -392-4·3·(-204)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-63}{2*3}=\frac{-24}{6}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+63}{2*3}=\frac{102}{6}
=17
$