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

Solution for (-3+7i)(1-6i)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-42i^2+25i-3=0

a = -42; b = 25; c = -3;
Δ = b2-4ac
Δ = 252-4·(-42)·(-3)
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*-42}=\frac{-36}{-84}
=3/7
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+11}{2*-42}=\frac{-14}{-84}
=1/6
$