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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-42i^2-36i+49i+42)=0

We get rid of parentheses

-42i^2-36i+49i+42=0

We add all the numbers together, and all the variables

-42i^2+13i+42=0

a = -42; b = 13; c = +42;
Δ = b2-4ac
Δ = 132-4·(-42)·42
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-85}{2*-42}=\frac{-98}{-84}
=1+1/6
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+85}{2*-42}=\frac{72}{-84}
=-6/7
$