(5+2i)(3-6i)=0

Solution for (5+2i)(3-6i)=0 equation:

(5+2i)(3-6i)=0

We add all the numbers together, and all the variables

(2i+5)(-6i+3)=0

We multiply parentheses ..

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

We get rid of parentheses

-12i^2+6i-30i+15=0

We add all the numbers together, and all the variables

-12i^2-24i+15=0

a = -12; b = -24; c = +15;
Δ = b2-4ac
Δ = -242-4·(-12)·15
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*-12}=\frac{-12}{-24}
=1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*-12}=\frac{60}{-24}
=-2+1/2
$