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

Solution for (x(1+i))(x(1-i))=0 equation:

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

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

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

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

Reorder the terms:
((1ix2 + -1i2x2) + 1x * (-1ix + 1x)) = 0
((1ix2 + -1i2x2) + 1x * (-1ix + 1x)) = 0
(1ix2 + -1i2x2 + (-1ix * 1x + 1x * 1x)) = 0
(1ix2 + -1i2x2 + (-1ix2 + 1x2)) = 0

Reorder the terms:
(1ix2 + -1ix2 + -1i2x2 + 1x2) = 0

Combine like terms: 1ix2 + -1ix2 = 0
(0 + -1i2x2 + 1x2) = 0
(-1i2x2 + 1x2) = 0

Solving
-1i2x2 + 1x2 = 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.
-1i2x2 + 1x2 + -1x2 = 0 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-1i2x2 + 0 = 0 + -1x2
-1i2x2 = 0 + -1x2
Remove the zero:
-1i2x2 = -1x2

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

Simplifying
i2 = 1

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