9+3i(7-2i)=0

Solution for 9+3i(7-2i)=0 equation:

9+3i(7-2i)=0

We add all the numbers together, and all the variables

3i(-2i+7)+9=0

We multiply parentheses

-6i^2+21i+9=0

a = -6; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·(-6)·9
Δ = 657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{73}}{2*-6}=\frac{-21-3\sqrt{73}}{-12}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{73}}{2*-6}=\frac{-21+3\sqrt{73}}{-12}
$