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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-7i^2-6i+42i+36)=0

We get rid of parentheses

-7i^2-6i+42i+36=0

We add all the numbers together, and all the variables

-7i^2+36i+36=0

a = -7; b = 36; c = +36;
Δ = b2-4ac
Δ = 362-4·(-7)·36
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-48}{2*-7}=\frac{-84}{-14}
=+6
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+48}{2*-7}=\frac{12}{-14}
=-6/7
$