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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5z^2+33z+18=0

a = 5; b = 33; c = +18;
Δ = b2-4ac
Δ = 332-4·5·18
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-27}{2*5}=\frac{-60}{10}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+27}{2*5}=\frac{-6}{10}
=-3/5
$