(5z+8)(1+z)=0

Solution for (5z+8)(1+z)=0 equation:

(5z+8)(1+z)=0

We add all the numbers together, and all the variables

(5z+8)(z+1)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5z^2+13z+8=0

a = 5; b = 13; c = +8;
Δ = b2-4ac
Δ = 132-4·5·8
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*5}=\frac{-16}{10}
=-1+3/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*5}=\frac{-10}{10}
=-1
$