(6-z)(5z+3)=0

Solution for (6-z)(5z+3)=0 equation:

(6-z)(5z+3)=0

We add all the numbers together, and all the variables

(-1z+6)(5z+3)=0

We multiply parentheses ..

(-5z^2-3z+30z+18)=0

We get rid of parentheses

-5z^2-3z+30z+18=0

We add all the numbers together, and all the variables

-5z^2+27z+18=0

a = -5; b = 27; c = +18;
Δ = b2-4ac
Δ = 272-4·(-5)·18
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-33}{2*-5}=\frac{-60}{-10}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+33}{2*-5}=\frac{6}{-10}
=-3/5
$