y^2+x^2-2y+8x-8x=0

Solution for y^2+x^2-2y+8x-8x=0 equation:

Simplifying
y2 + x2 + -2y + 8x + -8x = 0

Reorder the terms:
8x + -8x + x2 + -2y + y2 = 0

Combine like terms: 8x + -8x = 0
0 + x2 + -2y + y2 = 0
x2 + -2y + y2 = 0

Solving
x2 + -2y + y2 = 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 + 2y + y2 = 0 + 2y

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

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

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

Simplifying
x2 = 2y + -1y2

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

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

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

Factor a trinomial.
(x + -1y)(x + -1y) = 0

Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y
Subproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y
Solution
x = {y, y}