A+Z=AB^2+Z

Solution for A+Z=AB^2+Z equation:

Simplifying
A + Z = AB2 + Z

Add '-1Z' to each side of the equation.
A + Z + -1Z = AB2 + Z + -1Z

Combine like terms: Z + -1Z = 0
A + 0 = AB2 + Z + -1Z
A = AB2 + Z + -1Z

Combine like terms: Z + -1Z = 0
A = AB2 + 0
A = AB2

Solving
A = AB2

Solving for variable 'A'.

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

Add '-1AB2' to each side of the equation.
A + -1AB2 = AB2 + -1AB2

Combine like terms: AB2 + -1AB2 = 0
A + -1AB2 = 0

Factor out the Greatest Common Factor (GCF), 'A'.
A(1 + -1B2) = 0

Factor a difference between two squares.
A((1 + B)(1 + -1B)) = 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 + B)' equal to zero and attempt to solve:

Simplifying
1 + B = 0

Solving
1 + B = 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 + B = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -1B

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + -1B)' equal to zero and attempt to solve:

Simplifying
1 + -1B = 0

Solving
1 + -1B = 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 + -1B = 0 + -1

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

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

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

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

Simplifying
0 = -1 + B

The solution to this equation could not be determined.

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