(z+8)(z+9)=0

Solution for (z+8)(z+9)=0 equation:

(z+8)(z+9)=0

We multiply parentheses ..

(+z^2+9z+8z+72)=0

We get rid of parentheses

z^2+9z+8z+72=0

We add all the numbers together, and all the variables

z^2+17z+72=0

a = 1; b = 17; c = +72;
Δ = b2-4ac
Δ = 172-4·1·72
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-1}{2*1}=\frac{-18}{2}
=-9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+1}{2*1}=\frac{-16}{2}
=-8
$