(10+2i)(7-9i)=0

Solution for (10+2i)(7-9i)=0 equation:

(10+2i)(7-9i)=0

We add all the numbers together, and all the variables

(2i+10)(-9i+7)=0

We multiply parentheses ..

(-18i^2+14i-90i+70)=0

We get rid of parentheses

-18i^2+14i-90i+70=0

We add all the numbers together, and all the variables

-18i^2-76i+70=0

a = -18; b = -76; c = +70;
Δ = b2-4ac
Δ = -762-4·(-18)·70
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-104}{2*-18}=\frac{-28}{-36}
=7/9
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+104}{2*-18}=\frac{180}{-36}
=-5
$