(2-3i)(8+5i)=0

Solution for (2-3i)(8+5i)=0 equation:

(2-3i)(8+5i)=0

We add all the numbers together, and all the variables

(-3i+2)(5i+8)=0

We multiply parentheses ..

(-15i^2-24i+10i+16)=0

We get rid of parentheses

-15i^2-24i+10i+16=0

We add all the numbers together, and all the variables

-15i^2-14i+16=0

a = -15; b = -14; c = +16;
Δ = b2-4ac
Δ = -142-4·(-15)·16
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-34}{2*-15}=\frac{-20}{-30}
=2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+34}{2*-15}=\frac{48}{-30}
=-1+3/5
$