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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-15i^2+24i+63=0

a = -15; b = 24; c = +63;
Δ = b2-4ac
Δ = 242-4·(-15)·63
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-66}{2*-15}=\frac{-90}{-30}
=+3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+66}{2*-15}=\frac{42}{-30}
=-1+2/5
$