a^2-a^2=a^4-1

Solution for a^2-a^2=a^4-1 equation:

Simplifying
a2 + -1a2 = a4 + -1

Combine like terms: a2 + -1a2 = 0
0 = a4 + -1

Reorder the terms:
0 = -1 + a4

Solving
0 = -1 + a4

Solving for variable 'a'.

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

Add '-1a4' to each side of the equation.
0 + -1a4 = -1 + a4 + -1a4
Remove the zero:
-1a4 = -1 + a4 + -1a4

Combine like terms: a4 + -1a4 = 0
-1a4 = -1 + 0
-1a4 = -1

Divide each side by '-1'.
a4 = 1

Simplifying
a4 = 1

Reorder the terms:
-1 + a4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + a4 = 0

Factor a difference between two squares.
(1 + a2)(-1 + a2) = 0

Factor a difference between two squares.
(1 + a2)((1 + a)(-1 + a)) = 0

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

Simplifying
1 + a2 = 0

Solving
1 + a2 = 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 + a2 = 0 + -1

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

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

Simplifying
a2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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
Subproblem 3
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 = {-1, 1}