a^2x=a(a+1)

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

Simplifying
a2x = a(a + 1)

Reorder the terms:
a2x = a(1 + a)
a2x = (1 * a + a * a)
a2x = (1a + a2)

Solving
a2x = 1a + a2

Solving for variable 'a'.

Reorder the terms:
-1a + -1a2 + a2x = 1a + a2 + -1a + -1a2

Reorder the terms:
-1a + -1a2 + a2x = 1a + -1a + a2 + -1a2

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

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + -1a + ax) = 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 + -1a + ax)' equal to zero and attempt to solve:

Simplifying
-1 + -1a + ax = 0

Solving
-1 + -1a + ax = 0

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

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

Reorder the terms:
-1 + 1 + -1a + ax = 0 + 1

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

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

The solution to this equation could not be determined.

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