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

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


Simplifying
4x2 + 4xy2 + y4 = 0

Reorder the terms:
4xy2 + 4x2 + y4 = 0

Solving
4xy2 + 4x2 + y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + y2)(2x + y2) = 0


Subproblem 1
Set the factor '(2x + y2)' equal to zero and attempt to solve:

Simplifying
2x + y2 = 0

Solving
2x + y2 = 0

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

Add '-1y2' to each side of the equation.
2x + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
2x + 0 = 0 + -1y2
2x = 0 + -1y2
Remove the zero:
2x = -1y2

Divide each side by '2'.
x = -0.5y2

Simplifying
x = -0.5y2

Subproblem 2
Set the factor '(2x + y2)' equal to zero and attempt to solve:

Simplifying
2x + y2 = 0

Solving
2x + y2 = 0

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

Add '-1y2' to each side of the equation.
2x + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
2x + 0 = 0 + -1y2
2x = 0 + -1y2
Remove the zero:
2x = -1y2

Divide each side by '2'.
x = -0.5y2

Simplifying
x = -0.5y2
Solution
x = {-0.5y2, -0.5y2}

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