(x+i)(x-i)=0

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

Simplifying
(x + i)(x + -1i) = 0

Reorder the terms:
(i + x)(x + -1i) = 0

Reorder the terms:
(i + x)(-1i + x) = 0

Multiply (i + x) * (-1i + x)
(i(-1i + x) + x(-1i + x)) = 0
((-1i * i + x * i) + x(-1i + x)) = 0

Reorder the terms:
((ix + -1i2) + x(-1i + x)) = 0
((ix + -1i2) + x(-1i + x)) = 0
(ix + -1i2 + (-1i * x + x * x)) = 0
(ix + -1i2 + (-1ix + x2)) = 0

Reorder the terms:
(ix + -1ix + -1i2 + x2) = 0

Combine like terms: ix + -1ix = 0
(0 + -1i2 + x2) = 0
(-1i2 + x2) = 0

Solving
-1i2 + x2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1x2' to each side of the equation.
-1i2 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-1i2 + 0 = 0 + -1x2
-1i2 = 0 + -1x2
Remove the zero:
-1i2 = -1x2

Divide each side by '-1'.
i2 = x2

Simplifying
i2 = x2

Take the square root of each side:
i = {-1x, x}