a^2x(a-1)=(a+1)x

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Solution for a^2x(a-1)=(a+1)x equation: 


Simplifying
a2x(a + -1) = (a + 1) * x

Reorder the terms:
a2x(-1 + a) = (a + 1) * x
(-1 * a2x + a * a2x) = (a + 1) * x
(-1a2x + a3x) = (a + 1) * x

Reorder the terms:
-1a2x + a3x = (1 + a) * x

Reorder the terms for easier multiplication:
-1a2x + a3x = x(1 + a)
-1a2x + a3x = (1 * x + a * x)

Reorder the terms:
-1a2x + a3x = (ax + 1x)
-1a2x + a3x = (ax + 1x)

Solving
-1a2x + a3x = ax + 1x

Solving for variable 'a'.

Reorder the terms:
-1ax + -1a2x + a3x + -1x = ax + 1x + -1ax + -1x

Reorder the terms:
-1ax + -1a2x + a3x + -1x = ax + -1ax + 1x + -1x

Combine like terms: ax + -1ax = 0
-1ax + -1a2x + a3x + -1x = 0 + 1x + -1x
-1ax + -1a2x + a3x + -1x = 1x + -1x

Combine like terms: 1x + -1x = 0
-1ax + -1a2x + a3x + -1x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1a + -1a2 + a3 + -1) = 0


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

Simplifying
x = 0

Solving
x = 0

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

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

Simplifying
0 = -1x

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 '(-1a + -1a2 + a3 + -1)' equal to zero and attempt to solve:

Simplifying
-1a + -1a2 + a3 + -1 = 0

Reorder the terms:
-1 + -1a + -1a2 + a3 = 0

Solving
-1 + -1a + -1a2 + a3 = 0

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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