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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+35i^2-28i+20i-16)=0

We get rid of parentheses

35i^2-28i+20i-16=0

We add all the numbers together, and all the variables

35i^2-8i-16=0

a = 35; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·35·(-16)
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{-(-8)-48}{2*35}=\frac{-40}{70}
=-4/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+48}{2*35}=\frac{56}{70}
=4/5
$