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

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Solution for (x-4)(x(1+i))(x(1-i))=0 equation: 


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

Reorder the terms:
(-4 + x)(x(1 + i))(x(1 + -1i)) = 0
(-4 + x)((1 * x + i * x))(x(1 + -1i)) = 0

Reorder the terms:
(-4 + x)((ix + 1x))(x(1 + -1i)) = 0
(-4 + x)((ix + 1x))(x(1 + -1i)) = 0
(-4 + x)(ix + 1x)((1 * x + -1i * x)) = 0

Reorder the terms:
(-4 + x)(ix + 1x)((-1ix + 1x)) = 0
(-4 + x)(ix + 1x)((-1ix + 1x)) = 0

Multiply (-4 + x) * (ix + 1x)
(-4(ix + 1x) + x(ix + 1x))(-1ix + 1x) = 0
((ix * -4 + 1x * -4) + x(ix + 1x))(-1ix + 1x) = 0
((-4ix + -4x) + x(ix + 1x))(-1ix + 1x) = 0
(-4ix + -4x + (ix * x + 1x * x))(-1ix + 1x) = 0
(-4ix + -4x + (ix2 + 1x2))(-1ix + 1x) = 0

Reorder the terms:
(-4ix + ix2 + -4x + 1x2)(-1ix + 1x) = 0
(-4ix + ix2 + -4x + 1x2)(-1ix + 1x) = 0

Multiply (-4ix + ix2 + -4x + 1x2) * (-1ix + 1x)
(-4ix * (-1ix + 1x) + ix2(-1ix + 1x) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0
((-1ix * -4ix + 1x * -4ix) + ix2(-1ix + 1x) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0

Reorder the terms:
((-4ix2 + 4i2x2) + ix2(-1ix + 1x) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0
((-4ix2 + 4i2x2) + ix2(-1ix + 1x) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0
(-4ix2 + 4i2x2 + (-1ix * ix2 + 1x * ix2) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0

Reorder the terms:
(-4ix2 + 4i2x2 + (1ix3 + -1i2x3) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0
(-4ix2 + 4i2x2 + (1ix3 + -1i2x3) + -4x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0
(-4ix2 + 4i2x2 + 1ix3 + -1i2x3 + (-1ix * -4x + 1x * -4x) + 1x2 * (-1ix + 1x)) = 0
(-4ix2 + 4i2x2 + 1ix3 + -1i2x3 + (4ix2 + -4x2) + 1x2 * (-1ix + 1x)) = 0
(-4ix2 + 4i2x2 + 1ix3 + -1i2x3 + 4ix2 + -4x2 + (-1ix * 1x2 + 1x * 1x2)) = 0
(-4ix2 + 4i2x2 + 1ix3 + -1i2x3 + 4ix2 + -4x2 + (-1ix3 + 1x3)) = 0

Reorder the terms:
(-4ix2 + 4ix2 + 1ix3 + -1ix3 + 4i2x2 + -1i2x3 + -4x2 + 1x3) = 0

Combine like terms: -4ix2 + 4ix2 = 0
(0 + 1ix3 + -1ix3 + 4i2x2 + -1i2x3 + -4x2 + 1x3) = 0
(1ix3 + -1ix3 + 4i2x2 + -1i2x3 + -4x2 + 1x3) = 0

Combine like terms: 1ix3 + -1ix3 = 0
(0 + 4i2x2 + -1i2x3 + -4x2 + 1x3) = 0
(4i2x2 + -1i2x3 + -4x2 + 1x3) = 0

Solving
4i2x2 + -1i2x3 + -4x2 + 1x3 = 0

Solving for variable 'i'.

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

Add '4x2' to each side of the equation.
4i2x2 + -1i2x3 + -4x2 + 4x2 + 1x3 = 0 + 4x2

Combine like terms: -4x2 + 4x2 = 0
4i2x2 + -1i2x3 + 0 + 1x3 = 0 + 4x2
4i2x2 + -1i2x3 + 1x3 = 0 + 4x2
Remove the zero:
4i2x2 + -1i2x3 + 1x3 = 4x2

Add '-1x3' to each side of the equation.
4i2x2 + -1i2x3 + 1x3 + -1x3 = 4x2 + -1x3

Combine like terms: 1x3 + -1x3 = 0
4i2x2 + -1i2x3 + 0 = 4x2 + -1x3
4i2x2 + -1i2x3 = 4x2 + -1x3

Reorder the terms:
4i2x2 + -1i2x3 + -4x2 + x3 = 4x2 + -4x2 + -1x3 + x3

Combine like terms: 4x2 + -4x2 = 0
4i2x2 + -1i2x3 + -4x2 + x3 = 0 + -1x3 + x3
4i2x2 + -1i2x3 + -4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
4i2x2 + -1i2x3 + -4x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4i2 + -1i2x + -4 + x) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 = 0 + -1x2
Remove the zero:
0 = -1x2

Simplifying
0 = -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4i2 + -1i2x + -4 + x)' equal to zero and attempt to solve:

Simplifying
4i2 + -1i2x + -4 + x = 0

Reorder the terms:
-4 + 4i2 + -1i2x + x = 0

Solving
-4 + 4i2 + -1i2x + x = 0

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

Add '4' to each side of the equation.
-4 + 4i2 + -1i2x + 4 + x = 0 + 4

Reorder the terms:
-4 + 4 + 4i2 + -1i2x + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4i2 + -1i2x + x = 0 + 4
4i2 + -1i2x + x = 0 + 4

Combine like terms: 0 + 4 = 4
4i2 + -1i2x + x = 4

Add '-1x' to each side of the equation.
4i2 + -1i2x + x + -1x = 4 + -1x

Combine like terms: x + -1x = 0
4i2 + -1i2x + 0 = 4 + -1x
4i2 + -1i2x = 4 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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