(6-4i)(4+5i)=0

Solution for (6-4i)(4+5i)=0 equation:

(6-4i)(4+5i)=0

We add all the numbers together, and all the variables

(-4i+6)(5i+4)=0

We multiply parentheses ..

(-20i^2-16i+30i+24)=0

We get rid of parentheses

-20i^2-16i+30i+24=0

We add all the numbers together, and all the variables

-20i^2+14i+24=0

a = -20; b = 14; c = +24;
Δ = b2-4ac
Δ = 142-4·(-20)·24
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-46}{2*-20}=\frac{-60}{-40}
=1+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+46}{2*-20}=\frac{32}{-40}
=-4/5
$