81x-x^5=

Solution for 81x-x^5= equation:

Simplifying
81x + -1x5 = 0

Solving
81x + -1x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(81 + -1x4) = 0

Factor a difference between two squares.
x((9 + x2)(9 + -1x2)) = 0

Factor a difference between two squares.
x((9 + x2)((3 + x)(3 + -1x))) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

Solving
9 + x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 0 + -9
x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x2 = -9

Simplifying
x2 = -9

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}