(x^3-1)(x^3+1)=0

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Solution for (x^3-1)(x^3+1)=0 equation:


Simplifying
(x3 + -1)(x3 + 1) = 0

Reorder the terms:
(-1 + x3)(x3 + 1) = 0

Reorder the terms:
(-1 + x3)(1 + x3) = 0

Multiply (-1 + x3) * (1 + x3)
(-1(1 + x3) + x3(1 + x3)) = 0
((1 * -1 + x3 * -1) + x3(1 + x3)) = 0
((-1 + -1x3) + x3(1 + x3)) = 0
(-1 + -1x3 + (1 * x3 + x3 * x3)) = 0
(-1 + -1x3 + (1x3 + x6)) = 0

Combine like terms: -1x3 + 1x3 = 0
(-1 + 0 + x6) = 0
(-1 + x6) = 0

Solving
-1 + x6 = 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 + x6 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x6 = 0 + 1
x6 = 0 + 1

Combine like terms: 0 + 1 = 1
x6 = 1

Simplifying
x6 = 1

Reorder the terms:
-1 + x6 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x6 = 0

Factor a difference between two squares.
(1 + x3)(-1 + x3) = 0

Subproblem 1

Set the factor '(1 + x3)' equal to zero and attempt to solve: Simplifying 1 + x3 = 0 Solving 1 + x3 = 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 + x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = 0 + -1 x3 = 0 + -1 Combine like terms: 0 + -1 = -1 x3 = -1 Simplifying x3 = -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 + x3)' equal to zero and attempt to solve: Simplifying -1 + x3 = 0 Solving -1 + x3 = 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 + x3 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = 0 + 1 x3 = 0 + 1 Combine like terms: 0 + 1 = 1 x3 = 1 Simplifying x3 = 1 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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