[(x^3y^3+1)(x^3y^3-1)]=0

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

Simplifying
[(x3y3 + 1)(x3y3 + -1)] = 0

Reorder the terms:
[(1 + x3y3)(x3y3 + -1)] = 0

Reorder the terms:
[(1 + x3y3)(-1 + x3y3)] = 0

Multiply (1 + x3y3) * (-1 + x3y3)
[(1(-1 + x3y3) + x3y3(-1 + x3y3))] = 0
[((-1 * 1 + x3y3 * 1) + x3y3(-1 + x3y3))] = 0
[((-1 + 1x3y3) + x3y3(-1 + x3y3))] = 0
[(-1 + 1x3y3 + (-1 * x3y3 + x3y3 * x3y3))] = 0
[(-1 + 1x3y3 + (-1x3y3 + x6y6))] = 0

Combine like terms: 1x3y3 + -1x3y3 = 0
[(-1 + 0 + x6y6)] = 0
[(-1 + x6y6)] = 0
[-1 + x6y6] = 0

Remove brackets around [-1 + x6y6]
-1 + x6y6 = 0

Solving
-1 + x6y6 = 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 + x6y6 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x6y6 = 0 + 1
x6y6 = 0 + 1

Combine like terms: 0 + 1 = 1
x6y6 = 1

Divide each side by 'y6'.
x6 = y-6

Simplifying
x6 = y-6

Combine like terms: y-6 + -1y-6 = 0
x6 + -1y-6 = 0

Factor out the Greatest Common Factor (GCF), 'y-6'.
y-6(x6y6 + -1) = 0

Factor a difference between two squares.
y-6((x3y3 + 1)(x3y3 + -1)) = 0

Subproblem 1
Set the factor 'y-6' equal to zero and attempt to solve:

Simplifying
y-6 = 0

Solving
y-6 = 0

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

Add '-1y-6' to each side of the equation.
y-6 + -1y-6 = 0 + -1y-6
Remove the zero:
0 = -1y-6

Simplifying
0 = -1y-6

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 '(x3y3 + 1)' equal to zero and attempt to solve:

Simplifying
x3y3 + 1 = 0

Reorder the terms:
1 + x3y3 = 0

Solving
1 + x3y3 = 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 + x3y3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x3y3 = 0 + -1
x3y3 = 0 + -1

Combine like terms: 0 + -1 = -1
x3y3 = -1

Divide each side by 'y3'.
x3 = -1y-3

Simplifying
x3 = -1y-3

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 '(x3y3 + -1)' equal to zero and attempt to solve:

Simplifying
x3y3 + -1 = 0

Reorder the terms:
-1 + x3y3 = 0

Solving
-1 + x3y3 = 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 + x3y3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x3y3 = 0 + 1
x3y3 = 0 + 1

Combine like terms: 0 + 1 = 1
x3y3 = 1

Divide each side by 'y3'.
x3 = y-3

Simplifying
x3 = y-3

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.