(6-7i)(5+9i)=0

Solution for (6-7i)(5+9i)=0 equation:

(6-7i)(5+9i)=0

We add all the numbers together, and all the variables

(-7i+6)(9i+5)=0

We multiply parentheses ..

(-63i^2-35i+54i+30)=0

We get rid of parentheses

-63i^2-35i+54i+30=0

We add all the numbers together, and all the variables

-63i^2+19i+30=0

a = -63; b = 19; c = +30;
Δ = b2-4ac
Δ = 192-4·(-63)·30
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-89}{2*-63}=\frac{-108}{-126}
=6/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+89}{2*-63}=\frac{70}{-126}
=-5/9
$