12(5-7i)(2-i)=0

Solution for 12(5-7i)(2-i)=0 equation:

12(5-7i)(2-i)=0

We add all the numbers together, and all the variables

12(-7i+5)(-1i+2)=0

We multiply parentheses ..

12(+7i^2-14i-5i+10)=0

We multiply parentheses

84i^2-168i-60i+120=0

We add all the numbers together, and all the variables

84i^2-228i+120=0

a = 84; b = -228; c = +120;
Δ = b2-4ac
Δ = -2282-4·84·120
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-108}{2*84}=\frac{120}{168}
=5/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+108}{2*84}=\frac{336}{168}
=2
$