a(b^0)=a(b^2)

Solution for a(b^0)=a(b^2) equation:

Simplifying
a(b0) = a(b2)

Multiply a * 
a = a(b2)

Multiply a * b2
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}