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

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


Simplifying
a2b + -1a2 + -1b2 + 1 = (b + -1)(a2 + -1b + -1)

Reorder the terms:
1 + -1a2 + a2b + -1b2 = (b + -1)(a2 + -1b + -1)

Reorder the terms:
1 + -1a2 + a2b + -1b2 = (-1 + b)(a2 + -1b + -1)

Reorder the terms:
1 + -1a2 + a2b + -1b2 = (-1 + b)(-1 + a2 + -1b)

Multiply (-1 + b) * (-1 + a2 + -1b)
1 + -1a2 + a2b + -1b2 = (-1(-1 + a2 + -1b) + b(-1 + a2 + -1b))
1 + -1a2 + a2b + -1b2 = ((-1 * -1 + a2 * -1 + -1b * -1) + b(-1 + a2 + -1b))
1 + -1a2 + a2b + -1b2 = ((1 + -1a2 + 1b) + b(-1 + a2 + -1b))
1 + -1a2 + a2b + -1b2 = (1 + -1a2 + 1b + (-1 * b + a2 * b + -1b * b))

Reorder the terms:
1 + -1a2 + a2b + -1b2 = (1 + -1a2 + 1b + (a2b + -1b + -1b2))
1 + -1a2 + a2b + -1b2 = (1 + -1a2 + 1b + (a2b + -1b + -1b2))

Reorder the terms:
1 + -1a2 + a2b + -1b2 = (1 + -1a2 + a2b + 1b + -1b + -1b2)

Combine like terms: 1b + -1b = 0
1 + -1a2 + a2b + -1b2 = (1 + -1a2 + a2b + 0 + -1b2)
1 + -1a2 + a2b + -1b2 = (1 + -1a2 + a2b + -1b2)

Add '-1' to each side of the equation.
1 + -1a2 + a2b + -1 + -1b2 = 1 + -1a2 + a2b + -1 + -1b2

Reorder the terms:
1 + -1 + -1a2 + a2b + -1b2 = 1 + -1a2 + a2b + -1 + -1b2

Combine like terms: 1 + -1 = 0
0 + -1a2 + a2b + -1b2 = 1 + -1a2 + a2b + -1 + -1b2
-1a2 + a2b + -1b2 = 1 + -1a2 + a2b + -1 + -1b2

Reorder the terms:
-1a2 + a2b + -1b2 = 1 + -1 + -1a2 + a2b + -1b2

Combine like terms: 1 + -1 = 0
-1a2 + a2b + -1b2 = 0 + -1a2 + a2b + -1b2
-1a2 + a2b + -1b2 = -1a2 + a2b + -1b2

Add 'a2' to each side of the equation.
-1a2 + a2b + a2 + -1b2 = -1a2 + a2b + a2 + -1b2

Reorder the terms:
-1a2 + a2 + a2b + -1b2 = -1a2 + a2b + a2 + -1b2

Combine like terms: -1a2 + a2 = 0
0 + a2b + -1b2 = -1a2 + a2b + a2 + -1b2
a2b + -1b2 = -1a2 + a2b + a2 + -1b2

Reorder the terms:
a2b + -1b2 = -1a2 + a2 + a2b + -1b2

Combine like terms: -1a2 + a2 = 0
a2b + -1b2 = 0 + a2b + -1b2
a2b + -1b2 = a2b + -1b2

Add '-1a2b' to each side of the equation.
a2b + -1a2b + -1b2 = a2b + -1a2b + -1b2

Combine like terms: a2b + -1a2b = 0
0 + -1b2 = a2b + -1a2b + -1b2
-1b2 = a2b + -1a2b + -1b2

Combine like terms: a2b + -1a2b = 0
-1b2 = 0 + -1b2
-1b2 = -1b2

Add 'b2' to each side of the equation.
-1b2 + b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
0 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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