u^2-v^2-5u+5v=(u+v)(u-v)-5(u-v)

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Solution for u^2-v^2-5u+5v=(u+v)(u-v)-5(u-v) equation:


Simplifying
u2 + -1v2 + -5u + 5v = (u + v)(u + -1v) + -5(u + -1v)

Reorder the terms:
-5u + u2 + 5v + -1v2 = (u + v)(u + -1v) + -5(u + -1v)

Multiply (u + v) * (u + -1v)
-5u + u2 + 5v + -1v2 = (u(u + -1v) + v(u + -1v)) + -5(u + -1v)
-5u + u2 + 5v + -1v2 = ((u * u + -1v * u) + v(u + -1v)) + -5(u + -1v)

Reorder the terms:
-5u + u2 + 5v + -1v2 = ((-1uv + u2) + v(u + -1v)) + -5(u + -1v)
-5u + u2 + 5v + -1v2 = ((-1uv + u2) + v(u + -1v)) + -5(u + -1v)
-5u + u2 + 5v + -1v2 = (-1uv + u2 + (u * v + -1v * v)) + -5(u + -1v)
-5u + u2 + 5v + -1v2 = (-1uv + u2 + (uv + -1v2)) + -5(u + -1v)

Reorder the terms:
-5u + u2 + 5v + -1v2 = (-1uv + uv + u2 + -1v2) + -5(u + -1v)

Combine like terms: -1uv + uv = 0
-5u + u2 + 5v + -1v2 = (0 + u2 + -1v2) + -5(u + -1v)
-5u + u2 + 5v + -1v2 = (u2 + -1v2) + -5(u + -1v)
-5u + u2 + 5v + -1v2 = u2 + -1v2 + (u * -5 + -1v * -5)
-5u + u2 + 5v + -1v2 = u2 + -1v2 + (-5u + 5v)

Reorder the terms:
-5u + u2 + 5v + -1v2 = -5u + u2 + 5v + -1v2

Add '5u' to each side of the equation.
-5u + u2 + 5v + 5u + -1v2 = -5u + u2 + 5v + 5u + -1v2

Reorder the terms:
-5u + 5u + u2 + 5v + -1v2 = -5u + u2 + 5v + 5u + -1v2

Combine like terms: -5u + 5u = 0
0 + u2 + 5v + -1v2 = -5u + u2 + 5v + 5u + -1v2
u2 + 5v + -1v2 = -5u + u2 + 5v + 5u + -1v2

Reorder the terms:
u2 + 5v + -1v2 = -5u + 5u + u2 + 5v + -1v2

Combine like terms: -5u + 5u = 0
u2 + 5v + -1v2 = 0 + u2 + 5v + -1v2
u2 + 5v + -1v2 = u2 + 5v + -1v2

Add '-1u2' to each side of the equation.
u2 + 5v + -1u2 + -1v2 = u2 + 5v + -1u2 + -1v2

Reorder the terms:
u2 + -1u2 + 5v + -1v2 = u2 + 5v + -1u2 + -1v2

Combine like terms: u2 + -1u2 = 0
0 + 5v + -1v2 = u2 + 5v + -1u2 + -1v2
5v + -1v2 = u2 + 5v + -1u2 + -1v2

Reorder the terms:
5v + -1v2 = u2 + -1u2 + 5v + -1v2

Combine like terms: u2 + -1u2 = 0
5v + -1v2 = 0 + 5v + -1v2
5v + -1v2 = 5v + -1v2

Add '-5v' to each side of the equation.
5v + -5v + -1v2 = 5v + -5v + -1v2

Combine like terms: 5v + -5v = 0
0 + -1v2 = 5v + -5v + -1v2
-1v2 = 5v + -5v + -1v2

Combine like terms: 5v + -5v = 0
-1v2 = 0 + -1v2
-1v2 = -1v2

Add 'v2' to each side of the equation.
-1v2 + v2 = -1v2 + v2

Combine like terms: -1v2 + v2 = 0
0 = -1v2 + v2

Combine like terms: -1v2 + v2 = 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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