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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+18i^2-36i-6i+12)=0

We get rid of parentheses

18i^2-36i-6i+12=0

We add all the numbers together, and all the variables

18i^2-42i+12=0

a = 18; b = -42; c = +12;
Δ = b2-4ac
Δ = -422-4·18·12
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30}{2*18}=\frac{12}{36}
=1/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30}{2*18}=\frac{72}{36}
=2
$