(15-6i+30i+12)(-2i+6)=0

Solution for (15-6i+30i+12)(-2i+6)=0 equation:

(15-6i+30i+12)(-2i+6)=0

We add all the numbers together, and all the variables

(24i+27)(-2i+6)=0

We multiply parentheses ..

(-48i^2+144i-54i+162)=0

We get rid of parentheses

-48i^2+144i-54i+162=0

We add all the numbers together, and all the variables

-48i^2+90i+162=0

a = -48; b = 90; c = +162;
Δ = b2-4ac
Δ = 902-4·(-48)·162
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-198}{2*-48}=\frac{-288}{-96}
=+3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+198}{2*-48}=\frac{108}{-96}
=-1+1/8
$