(x^2-a^2+2a-1)+(2x+2a-2)=1-2a+a^2-x^2

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Solution for (x^2-a^2+2a-1)+(2x+2a-2)=1-2a+a^2-x^2 equation: 


Simplifying
(x2 + -1a2 + 2a + -1) + (2x + 2a + -2) = 1 + -2a + a2 + -1x2

Reorder the terms:
(-1 + 2a + -1a2 + x2) + (2x + 2a + -2) = 1 + -2a + a2 + -1x2

Remove parenthesis around (-1 + 2a + -1a2 + x2)
-1 + 2a + -1a2 + x2 + (2x + 2a + -2) = 1 + -2a + a2 + -1x2

Reorder the terms:
-1 + 2a + -1a2 + x2 + (-2 + 2a + 2x) = 1 + -2a + a2 + -1x2

Remove parenthesis around (-2 + 2a + 2x)
-1 + 2a + -1a2 + x2 + -2 + 2a + 2x = 1 + -2a + a2 + -1x2

Reorder the terms:
-1 + -2 + 2a + 2a + -1a2 + 2x + x2 = 1 + -2a + a2 + -1x2

Combine like terms: -1 + -2 = -3
-3 + 2a + 2a + -1a2 + 2x + x2 = 1 + -2a + a2 + -1x2

Combine like terms: 2a + 2a = 4a
-3 + 4a + -1a2 + 2x + x2 = 1 + -2a + a2 + -1x2

Solving
-3 + 4a + -1a2 + 2x + x2 = 1 + -2a + a2 + -1x2

Solving for variable 'a'.

Reorder the terms:
-3 + -1 + 4a + 2a + -1a2 + -1a2 + 2x + x2 + x2 = 1 + -2a + a2 + -1x2 + -1 + 2a + -1a2 + x2

Combine like terms: -3 + -1 = -4
-4 + 4a + 2a + -1a2 + -1a2 + 2x + x2 + x2 = 1 + -2a + a2 + -1x2 + -1 + 2a + -1a2 + x2

Combine like terms: 4a + 2a = 6a
-4 + 6a + -1a2 + -1a2 + 2x + x2 + x2 = 1 + -2a + a2 + -1x2 + -1 + 2a + -1a2 + x2

Combine like terms: -1a2 + -1a2 = -2a2
-4 + 6a + -2a2 + 2x + x2 + x2 = 1 + -2a + a2 + -1x2 + -1 + 2a + -1a2 + x2

Combine like terms: x2 + x2 = 2x2
-4 + 6a + -2a2 + 2x + 2x2 = 1 + -2a + a2 + -1x2 + -1 + 2a + -1a2 + x2

Reorder the terms:
-4 + 6a + -2a2 + 2x + 2x2 = 1 + -1 + -2a + 2a + a2 + -1a2 + -1x2 + x2

Combine like terms: 1 + -1 = 0
-4 + 6a + -2a2 + 2x + 2x2 = 0 + -2a + 2a + a2 + -1a2 + -1x2 + x2
-4 + 6a + -2a2 + 2x + 2x2 = -2a + 2a + a2 + -1a2 + -1x2 + x2

Combine like terms: -2a + 2a = 0
-4 + 6a + -2a2 + 2x + 2x2 = 0 + a2 + -1a2 + -1x2 + x2
-4 + 6a + -2a2 + 2x + 2x2 = a2 + -1a2 + -1x2 + x2

Combine like terms: a2 + -1a2 = 0
-4 + 6a + -2a2 + 2x + 2x2 = 0 + -1x2 + x2
-4 + 6a + -2a2 + 2x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4 + 6a + -2a2 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3a + -1a2 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 3a + -1a2 + x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 3a + -1a2 + x + x2 = 0

Solving
-2 + 3a + -1a2 + x + x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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