(z+3)(z+-7)=0

Solution for (z+3)(z+-7)=0 equation:

(z+3)(z+-7)=0

We add all the numbers together, and all the variables

(z+3)(z-7)=0

We multiply parentheses ..

(+z^2-7z+3z-21)=0

We get rid of parentheses

z^2-7z+3z-21=0

We add all the numbers together, and all the variables

z^2-4z-21=0

a = 1; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*1}=\frac{-6}{2}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*1}=\frac{14}{2}
=7
$