ax=a^3x

Solution for ax=a^3x equation:

Simplifying
ax = a3x

Solving
ax = a3x

Solving for variable 'a'.

Combine like terms: a3x + -1a3x = 0
ax + -1a3x = 0

Factor out the Greatest Common Factor (GCF), 'ax'.
ax(1 + -1a2) = 0

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

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

Simplifying
ax = 0

Solving
ax = 0

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

Simplifying
ax = 0

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 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

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

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 1

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