(5z+3)(2+z)=0

Solution for (5z+3)(2+z)=0 equation:

(5z+3)(2+z)=0

We add all the numbers together, and all the variables

(5z+3)(z+2)=0

We multiply parentheses ..

(+5z^2+10z+3z+6)=0

We get rid of parentheses

5z^2+10z+3z+6=0

We add all the numbers together, and all the variables

5z^2+13z+6=0

a = 5; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·5·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*5}=\frac{-20}{10}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*5}=\frac{-6}{10}
=-3/5
$