3z(12+5z)=0

Solution for 3z(12+5z)=0 equation:

3z(12+5z)=0

We add all the numbers together, and all the variables

3z(5z+12)=0

We multiply parentheses

15z^2+36z=0

a = 15; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·15·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*15}=\frac{-72}{30}
=-2+2/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*15}=\frac{0}{30}
=0
$