x^2-y^2=(x+y)(x-y)

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


Simplifying
x2 + -1y2 = (x + y)(x + -1y)

Multiply (x + y) * (x + -1y)
x2 + -1y2 = (x(x + -1y) + y(x + -1y))
x2 + -1y2 = ((x * x + -1y * x) + y(x + -1y))

Reorder the terms:
x2 + -1y2 = ((-1xy + x2) + y(x + -1y))
x2 + -1y2 = ((-1xy + x2) + y(x + -1y))
x2 + -1y2 = (-1xy + x2 + (x * y + -1y * y))
x2 + -1y2 = (-1xy + x2 + (xy + -1y2))

Reorder the terms:
x2 + -1y2 = (-1xy + xy + x2 + -1y2)

Combine like terms: -1xy + xy = 0
x2 + -1y2 = (0 + x2 + -1y2)
x2 + -1y2 = (x2 + -1y2)

Add '-1x2' to each side of the equation.
x2 + -1x2 + -1y2 = x2 + -1x2 + -1y2

Combine like terms: x2 + -1x2 = 0
0 + -1y2 = x2 + -1x2 + -1y2
-1y2 = x2 + -1x2 + -1y2

Combine like terms: x2 + -1x2 = 0
-1y2 = 0 + -1y2
-1y2 = -1y2

Add 'y2' to each side of the equation.
-1y2 + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -1y2 + y2

Combine like terms: -1y2 + y2 = 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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