4x^2+4y^2-8y=0

Solution for 4x^2+4y^2-8y=0 equation:

Simplifying
4x2 + 4y2 + -8y = 0

Reorder the terms:
4x2 + -8y + 4y2 = 0

Solving
4x2 + -8y + 4y2 = 0

Solving for variable 'x'.

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

Add '8y' to each side of the equation.
4x2 + -8y + 8y + 4y2 = 0 + 8y

Combine like terms: -8y + 8y = 0
4x2 + 0 + 4y2 = 0 + 8y
4x2 + 4y2 = 0 + 8y
Remove the zero:
4x2 + 4y2 = 8y

Add '-4y2' to each side of the equation.
4x2 + 4y2 + -4y2 = 8y + -4y2

Combine like terms: 4y2 + -4y2 = 0
4x2 + 0 = 8y + -4y2
4x2 = 8y + -4y2

Divide each side by '4'.
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}