(2+3i)(2*i)=0

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

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

We add all the numbers together, and all the variables

(3i+2)2i=0

We multiply parentheses

6i^2+4i=0

a = 6; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·6·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*6}=\frac{-8}{12}
=-2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*6}=\frac{0}{12}
=0
$