(x^4+1)(x^2+1)(x+1)(x-1)=

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Solution for (x^4+1)(x^2+1)(x+1)(x-1)= equation: 


Simplifying
(x4 + 1)(x2 + 1)(x + 1)(x + -1) = 0

Reorder the terms:
(1 + x4)(x2 + 1)(x + 1)(x + -1) = 0

Reorder the terms:
(1 + x4)(1 + x2)(x + 1)(x + -1) = 0

Reorder the terms:
(1 + x4)(1 + x2)(1 + x)(x + -1) = 0

Reorder the terms:
(1 + x4)(1 + x2)(1 + x)(-1 + x) = 0

Multiply (1 + x4) * (1 + x2)
(1(1 + x2) + x4(1 + x2))(1 + x)(-1 + x) = 0
((1 * 1 + x2 * 1) + x4(1 + x2))(1 + x)(-1 + x) = 0
((1 + 1x2) + x4(1 + x2))(1 + x)(-1 + x) = 0
(1 + 1x2 + (1 * x4 + x2 * x4))(1 + x)(-1 + x) = 0
(1 + 1x2 + (1x4 + x6))(1 + x)(-1 + x) = 0
(1 + 1x2 + 1x4 + x6)(1 + x)(-1 + x) = 0

Multiply (1 + 1x2 + 1x4 + x6) * (1 + x)
(1(1 + x) + 1x2 * (1 + x) + 1x4 * (1 + x) + x6(1 + x))(-1 + x) = 0
((1 * 1 + x * 1) + 1x2 * (1 + x) + 1x4 * (1 + x) + x6(1 + x))(-1 + x) = 0
((1 + 1x) + 1x2 * (1 + x) + 1x4 * (1 + x) + x6(1 + x))(-1 + x) = 0
(1 + 1x + (1 * 1x2 + x * 1x2) + 1x4 * (1 + x) + x6(1 + x))(-1 + x) = 0
(1 + 1x + (1x2 + 1x3) + 1x4 * (1 + x) + x6(1 + x))(-1 + x) = 0
(1 + 1x + 1x2 + 1x3 + (1 * 1x4 + x * 1x4) + x6(1 + x))(-1 + x) = 0
(1 + 1x + 1x2 + 1x3 + (1x4 + 1x5) + x6(1 + x))(-1 + x) = 0
(1 + 1x + 1x2 + 1x3 + 1x4 + 1x5 + (1 * x6 + x * x6))(-1 + x) = 0
(1 + 1x + 1x2 + 1x3 + 1x4 + 1x5 + (1x6 + x7))(-1 + x) = 0
(1 + 1x + 1x2 + 1x3 + 1x4 + 1x5 + 1x6 + x7)(-1 + x) = 0

Multiply (1 + 1x + 1x2 + 1x3 + 1x4 + 1x5 + 1x6 + x7) * (-1 + x)
(1(-1 + x) + 1x * (-1 + x) + 1x2 * (-1 + x) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
((-1 * 1 + x * 1) + 1x * (-1 + x) + 1x2 * (-1 + x) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
((-1 + 1x) + 1x * (-1 + x) + 1x2 * (-1 + x) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + (-1 * 1x + x * 1x) + 1x2 * (-1 + x) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + (-1x + 1x2) + 1x2 * (-1 + x) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + (-1 * 1x2 + x * 1x2) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + (-1x2 + 1x3) + 1x3 * (-1 + x) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + (-1 * 1x3 + x * 1x3) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + (-1x3 + 1x4) + 1x4 * (-1 + x) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + (-1 * 1x4 + x * 1x4) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + (-1x4 + 1x5) + 1x5 * (-1 + x) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + (-1 * 1x5 + x * 1x5) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + (-1x5 + 1x6) + 1x6 * (-1 + x) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + (-1 * 1x6 + x * 1x6) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + (-1x6 + 1x7) + x7(-1 + x)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + (-1 * x7 + x * x7)) = 0
(-1 + 1x + -1x + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + (-1x7 + x8)) = 0

Combine like terms: 1x + -1x = 0
(-1 + 0 + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0
(-1 + 1x2 + -1x2 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0

Combine like terms: 1x2 + -1x2 = 0
(-1 + 0 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0
(-1 + 1x3 + -1x3 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0

Combine like terms: 1x3 + -1x3 = 0
(-1 + 0 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0
(-1 + 1x4 + -1x4 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0

Combine like terms: 1x4 + -1x4 = 0
(-1 + 0 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0
(-1 + 1x5 + -1x5 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0

Combine like terms: 1x5 + -1x5 = 0
(-1 + 0 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0
(-1 + 1x6 + -1x6 + 1x7 + -1x7 + x8) = 0

Combine like terms: 1x6 + -1x6 = 0
(-1 + 0 + 1x7 + -1x7 + x8) = 0
(-1 + 1x7 + -1x7 + x8) = 0

Combine like terms: 1x7 + -1x7 = 0
(-1 + 0 + x8) = 0
(-1 + x8) = 0

Solving
-1 + x8 = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x8 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x8 = 0 + 1
x8 = 0 + 1

Combine like terms: 0 + 1 = 1
x8 = 1

Simplifying
x8 = 1

Reorder the terms:
-1 + x8 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x8 = 0

Factor a difference between two squares.
(1 + x4)(-1 + x4) = 0

Factor a difference between two squares.
(1 + x4)((1 + x2)(-1 + x2)) = 0

Factor a difference between two squares.
(1 + x4)((1 + x2)((1 + x)(-1 + x))) = 0


Subproblem 1
Set the factor '(1 + x4)' equal to zero and attempt to solve:

Simplifying
1 + x4 = 0

Solving
1 + x4 = 0

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

Add '-1' to each side of the equation.
1 + -1 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x4 = 0 + -1
x4 = 0 + -1

Combine like terms: 0 + -1 = -1
x4 = -1

Simplifying
x4 = -1

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 '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {-1, 1}

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