a^3-1=a^2-1

Solution for a^3-1=a^2-1 equation:

Simplifying
a3 + -1 = a2 + -1

Reorder the terms:
-1 + a3 = a2 + -1

Reorder the terms:
-1 + a3 = -1 + a2

Add '1' to each side of the equation.
-1 + 1 + a3 = -1 + 1 + a2

Combine like terms: -1 + 1 = 0
0 + a3 = -1 + 1 + a2
a3 = -1 + 1 + a2

Combine like terms: -1 + 1 = 0
a3 = 0 + a2
a3 = a2

Solving
a3 = a2

Solving for variable 'a'.

Reorder the terms:
-1a2 + a3 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-1a2 + a3 = 0

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(-1 + a) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-1 + a)' equal to zero and attempt to solve:

Simplifying
-1 + a = 0

Solving
-1 + a = 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 + a = 0 + 1

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

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

Simplifying
a = 1
Solution
a = {0, 1}