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

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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 + y)(x + y) = 0

Subproblem 1

Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1y

Subproblem 2

Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1y

Solution

x = {-1y, -1y}

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