81x^3-u^4x^3=0

Solution for 81x^3-u^4x^3=0 equation:

Simplifying
81x3 + -1u4x3 = 0

Reorder the terms:
-1u4x3 + 81x3 = 0

Solving
-1u4x3 + 81x3 = 0

Solving for variable 'u'.

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

Add '-81x3' to each side of the equation.
-1u4x3 + 81x3 + -81x3 = 0 + -81x3

Combine like terms: 81x3 + -81x3 = 0
-1u4x3 + 0 = 0 + -81x3
-1u4x3 = 0 + -81x3
Remove the zero:
-1u4x3 = -81x3

Divide each side by '-1x3'.
u4 = 81

Simplifying
u4 = 81

Reorder the terms:
-81 + u4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + u4 = 0

Factor a difference between two squares.
(9 + u2)(-9 + u2) = 0

Factor a difference between two squares.
(9 + u2)((3 + u)(-3 + u)) = 0

Subproblem 1
Set the factor '(9 + u2)' equal to zero and attempt to solve:

Simplifying
9 + u2 = 0

Solving
9 + u2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + u2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + u2 = 0 + -9
u2 = 0 + -9

Combine like terms: 0 + -9 = -9
u2 = -9

Simplifying
u2 = -9

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 '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Subproblem 3
Set the factor '(-3 + u)' equal to zero and attempt to solve:

Simplifying
-3 + u = 0

Solving
-3 + u = 0

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

Add '3' to each side of the equation.
-3 + 3 + u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + u = 0 + 3
u = 0 + 3

Combine like terms: 0 + 3 = 3
u = 3

Simplifying
u = 3
Solution
u = {-3, 3}