(5+z)(5z+8)=0

Solution for (5+z)(5z+8)=0 equation:

(5+z)(5z+8)=0

We add all the numbers together, and all the variables

(z+5)(5z+8)=0

We multiply parentheses ..

(+5z^2+8z+25z+40)=0

We get rid of parentheses

5z^2+8z+25z+40=0

We add all the numbers together, and all the variables

5z^2+33z+40=0

a = 5; b = 33; c = +40;
Δ = b2-4ac
Δ = 332-4·5·40
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-17}{2*5}=\frac{-50}{10}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+17}{2*5}=\frac{-16}{10}
=-1+3/5
$