(4-6i)(3+7i)=0

Solution for (4-6i)(3+7i)=0 equation:

(4-6i)(3+7i)=0

We add all the numbers together, and all the variables

(-6i+4)(7i+3)=0

We multiply parentheses ..

(-42i^2-18i+28i+12)=0

We get rid of parentheses

-42i^2-18i+28i+12=0

We add all the numbers together, and all the variables

-42i^2+10i+12=0

a = -42; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·(-42)·12
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-46}{2*-42}=\frac{-56}{-84}
=2/3
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+46}{2*-42}=\frac{36}{-84}
=-3/7
$