x^2+y^2-z^2-2y+2z=0

Solution for x^2+y^2-z^2-2y+2z=0 equation:

Simplifying
x2 + y2 + -1z2 + -2y + 2z = 0

Reorder the terms:
x2 + -2y + y2 + 2z + -1z2 = 0

Solving
x2 + -2y + y2 + 2z + -1z2 = 0

Solving for variable 'x'.

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

Add '2y' to each side of the equation.
x2 + -2y + y2 + 2z + 2y + -1z2 = 0 + 2y

Reorder the terms:
x2 + -2y + 2y + y2 + 2z + -1z2 = 0 + 2y

Combine like terms: -2y + 2y = 0
x2 + 0 + y2 + 2z + -1z2 = 0 + 2y
x2 + y2 + 2z + -1z2 = 0 + 2y
Remove the zero:
x2 + y2 + 2z + -1z2 = 2y

Add '-1y2' to each side of the equation.
x2 + y2 + 2z + -1y2 + -1z2 = 2y + -1y2

Reorder the terms:
x2 + y2 + -1y2 + 2z + -1z2 = 2y + -1y2

Combine like terms: y2 + -1y2 = 0
x2 + 0 + 2z + -1z2 = 2y + -1y2
x2 + 2z + -1z2 = 2y + -1y2

Add '-2z' to each side of the equation.
x2 + 2z + -2z + -1z2 = 2y + -1y2 + -2z

Combine like terms: 2z + -2z = 0
x2 + 0 + -1z2 = 2y + -1y2 + -2z
x2 + -1z2 = 2y + -1y2 + -2z

Add 'z2' to each side of the equation.
x2 + -1z2 + z2 = 2y + -1y2 + -2z + z2

Combine like terms: -1z2 + z2 = 0
x2 + 0 = 2y + -1y2 + -2z + z2
x2 = 2y + -1y2 + -2z + z2

Simplifying
x2 = 2y + -1y2 + -2z + z2

Reorder the terms:
x2 + -2y + y2 + 2z + -1z2 = 2y + -2y + -1y2 + y2 + -2z + 2z + z2 + -1z2

Combine like terms: 2y + -2y = 0
x2 + -2y + y2 + 2z + -1z2 = 0 + -1y2 + y2 + -2z + 2z + z2 + -1z2
x2 + -2y + y2 + 2z + -1z2 = -1y2 + y2 + -2z + 2z + z2 + -1z2

Combine like terms: -1y2 + y2 = 0
x2 + -2y + y2 + 2z + -1z2 = 0 + -2z + 2z + z2 + -1z2
x2 + -2y + y2 + 2z + -1z2 = -2z + 2z + z2 + -1z2

Combine like terms: -2z + 2z = 0
x2 + -2y + y2 + 2z + -1z2 = 0 + z2 + -1z2
x2 + -2y + y2 + 2z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + -2y + y2 + 2z + -1z2 = 0

The solution to this equation could not be determined.