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

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

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

We add all the numbers together, and all the variables

(7i+3)(-1i+3)=0

We multiply parentheses ..

(-7i^2+21i-3i+9)=0

We get rid of parentheses

-7i^2+21i-3i+9=0

We add all the numbers together, and all the variables

-7i^2+18i+9=0

a = -7; b = 18; c = +9;
Δ = b2-4ac
Δ = 182-4·(-7)·9
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*-7}=\frac{-42}{-14}
=+3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*-7}=\frac{6}{-14}
=-3/7
$