(7-3i)(6-i)=0

Solution for (7-3i)(6-i)=0 equation:

(7-3i)(6-i)=0

We add all the numbers together, and all the variables

(-3i+7)(-1i+6)=0

We multiply parentheses ..

(+3i^2-18i-7i+42)=0

We get rid of parentheses

3i^2-18i-7i+42=0

We add all the numbers together, and all the variables

3i^2-25i+42=0

a = 3; b = -25; c = +42;
Δ = b2-4ac
Δ = -252-4·3·42
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11}{2*3}=\frac{14}{6}
=2+1/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11}{2*3}=\frac{36}{6}
=6
$