(7-5i)(-3+9i)=0

Solution for (7-5i)(-3+9i)=0 equation:

(7-5i)(-3+9i)=0

We add all the numbers together, and all the variables

(-5i+7)(9i-3)=0

We multiply parentheses ..

(-45i^2+15i+63i-21)=0

We get rid of parentheses

-45i^2+15i+63i-21=0

We add all the numbers together, and all the variables

-45i^2+78i-21=0

a = -45; b = 78; c = -21;
Δ = b2-4ac
Δ = 782-4·(-45)·(-21)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-48}{2*-45}=\frac{-126}{-90}
=1+2/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+48}{2*-45}=\frac{-30}{-90}
=1/3
$