(7-2i)*(4-5i)=0

Solution for (7-2i)*(4-5i)=0 equation:

(7-2i)(4-5i)=0

We add all the numbers together, and all the variables

(-2i+7)(-5i+4)=0

We multiply parentheses ..

(+10i^2-8i-35i+28)=0

We get rid of parentheses

10i^2-8i-35i+28=0

We add all the numbers together, and all the variables

10i^2-43i+28=0

a = 10; b = -43; c = +28;
Δ = b2-4ac
Δ = -432-4·10·28
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-27}{2*10}=\frac{16}{20}
=4/5
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+27}{2*10}=\frac{70}{20}
=3+1/2
$