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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10i^2+31i+24=0

a = 10; b = 31; c = +24;
Δ = b2-4ac
Δ = 312-4·10·24
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-1}{2*10}=\frac{-32}{20}
=-1+3/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+1}{2*10}=\frac{-30}{20}
=-1+1/2
$