(4+i)(4-i)=0

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

(4+i)(4-i)=0

We add all the numbers together, and all the variables

(i+4)(-1i+4)=0

We multiply parentheses ..

(-1i^2+4i-4i+16)=0

We get rid of parentheses

-1i^2+4i-4i+16=0

We add all the numbers together, and all the variables

-1i^2+16=0

a = -1; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-1)·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-1}=\frac{-8}{-2}
=+4
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-1}=\frac{8}{-2}
=-4
$