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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-28i^2-24i+21i+18)=0

We get rid of parentheses

-28i^2-24i+21i+18=0

We add all the numbers together, and all the variables

-28i^2-3i+18=0

a = -28; b = -3; c = +18;
Δ = b2-4ac
Δ = -32-4·(-28)·18
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*-28}=\frac{-42}{-56}
=3/4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*-28}=\frac{48}{-56}
=-6/7
$