(2-5i)(8+6i)=0

Solution for (2-5i)(8+6i)=0 equation:

(2-5i)(8+6i)=0

We add all the numbers together, and all the variables

(-5i+2)(6i+8)=0

We multiply parentheses ..

(-30i^2-40i+12i+16)=0

We get rid of parentheses

-30i^2-40i+12i+16=0

We add all the numbers together, and all the variables

-30i^2-28i+16=0

a = -30; b = -28; c = +16;
Δ = b2-4ac
Δ = -282-4·(-30)·16
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-52}{2*-30}=\frac{-24}{-60}
=2/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+52}{2*-30}=\frac{80}{-60}
=-1+1/3
$