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

Solution for (5+i)(2-2i)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2i^2+2i-10i+10)=0

We get rid of parentheses

-2i^2+2i-10i+10=0

We add all the numbers together, and all the variables

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

a = -2; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-2}=\frac{-4}{-4}
=1
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-2}=\frac{20}{-4}
=-5
$