(9-6i)(6+i)=0

Solution for (9-6i)(6+i)=0 equation:

(9-6i)(6+i)=0

We add all the numbers together, and all the variables

(-6i+9)(i+6)=0

We multiply parentheses ..

(-6i^2-36i+9i+54)=0

We get rid of parentheses

-6i^2-36i+9i+54=0

We add all the numbers together, and all the variables

-6i^2-27i+54=0

a = -6; b = -27; c = +54;
Δ = b2-4ac
Δ = -272-4·(-6)·54
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-45}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+45}{2*-6}=\frac{72}{-12}
=-6
$