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

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

Simplifying
a2(a + -1) * x = a(a + 1 + 2x)

Reorder the terms:
a2(-1 + a) * x = a(a + 1 + 2x)

Reorder the terms for easier multiplication:
a2 * x(-1 + a) = a(a + 1 + 2x)

Multiply a2 * x
a2x(-1 + a) = a(a + 1 + 2x)
(-1 * a2x + a * a2x) = a(a + 1 + 2x)
(-1a2x + a3x) = a(a + 1 + 2x)

Reorder the terms:
-1a2x + a3x = a(1 + a + 2x)
-1a2x + a3x = (1 * a + a * a + 2x * a)

Reorder the terms:
-1a2x + a3x = (1a + 2ax + a2)
-1a2x + a3x = (1a + 2ax + a2)

Solving
-1a2x + a3x = 1a + 2ax + a2

Solving for variable 'a'.

Reorder the terms:
-1a + -2ax + -1a2 + -1a2x + a3x = 1a + 2ax + a2 + -1a + -2ax + -1a2

Reorder the terms:
-1a + -2ax + -1a2 + -1a2x + a3x = 1a + -1a + 2ax + -2ax + a2 + -1a2

Combine like terms: 1a + -1a = 0
-1a + -2ax + -1a2 + -1a2x + a3x = 0 + 2ax + -2ax + a2 + -1a2
-1a + -2ax + -1a2 + -1a2x + a3x = 2ax + -2ax + a2 + -1a2

Combine like terms: 2ax + -2ax = 0
-1a + -2ax + -1a2 + -1a2x + a3x = 0 + a2 + -1a2
-1a + -2ax + -1a2 + -1a2x + a3x = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-1a + -2ax + -1a2 + -1a2x + a3x = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + -2x + -1a + -1ax + a2x) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-1 + -2x + -1a + -1ax + a2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x + -1a + -1ax + a2x = 0

Reorder the terms:
-1 + -1a + -1ax + a2x + -2x = 0

Solving
-1 + -1a + -1ax + a2x + -2x = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}