a^2*x+a^2=ab+abx

Solution for a^2*x+a^2=ab+abx equation:

Simplifying
a2 * x + a2 = ab + abx

Multiply a2 * x
a2x + a2 = ab + abx

Reorder the terms:
a2 + a2x = ab + abx

Solving
a2 + a2x = ab + abx

Solving for variable 'a'.

Reorder the terms:
-1ab + -1abx + a2 + a2x = ab + abx + -1ab + -1abx

Reorder the terms:
-1ab + -1abx + a2 + a2x = ab + -1ab + abx + -1abx

Combine like terms: ab + -1ab = 0
-1ab + -1abx + a2 + a2x = 0 + abx + -1abx
-1ab + -1abx + a2 + a2x = abx + -1abx

Combine like terms: abx + -1abx = 0
-1ab + -1abx + a2 + a2x = 0

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

Simplifying
-1b + -1bx + a + ax = 0

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

Solving
a + ax + -1b + -1bx = 0

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

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

Combine like terms: -1b + b = 0
a + ax + 0 + -1bx = 0 + b
a + ax + -1bx = 0 + b
Remove the zero:
a + ax + -1bx = b

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

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

The solution to this equation could not be determined.

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