(4-5i)(6+2i)=0

Solution for (4-5i)(6+2i)=0 equation:

(4-5i)(6+2i)=0

We add all the numbers together, and all the variables

(-5i+4)(2i+6)=0

We multiply parentheses ..

(-10i^2-30i+8i+24)=0

We get rid of parentheses

-10i^2-30i+8i+24=0

We add all the numbers together, and all the variables

-10i^2-22i+24=0

a = -10; b = -22; c = +24;
Δ = b2-4ac
Δ = -222-4·(-10)·24
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-38}{2*-10}=\frac{-16}{-20}
=4/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+38}{2*-10}=\frac{60}{-20}
=-3
$