x^4-10x^2y^4+9y^8=0

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Solution for x^4-10x^2y^4+9y^8=0 equation: 


Simplifying
x4 + -10x2y4 + 9y8 = 0

Reorder the terms:
-10x2y4 + x4 + 9y8 = 0

Solving
-10x2y4 + x4 + 9y8 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -9y4)(x2 + -1y4) = 0

Factor a difference between two squares.
((x + 3y2)(x + -3y2))(x2 + -1y4) = 0

Factor a difference between two squares.
((x + y2)(x + -1y2))(x + 3y2)(x + -3y2) = 0


Subproblem 1
Set the factor '(x + 3y2)' equal to zero and attempt to solve:

Simplifying
x + 3y2 = 0

Solving
x + 3y2 = 0

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

Add '-3y2' to each side of the equation.
x + 3y2 + -3y2 = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
x + 0 = 0 + -3y2
x = 0 + -3y2
Remove the zero:
x = -3y2

Simplifying
x = -3y2

Subproblem 2
Set the factor '(x + -3y2)' equal to zero and attempt to solve:

Simplifying
x + -3y2 = 0

Solving
x + -3y2 = 0

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

Add '3y2' to each side of the equation.
x + -3y2 + 3y2 = 0 + 3y2

Combine like terms: -3y2 + 3y2 = 0
x + 0 = 0 + 3y2
x = 0 + 3y2
Remove the zero:
x = 3y2

Simplifying
x = 3y2

Subproblem 3
Set the factor '(x + y2)' equal to zero and attempt to solve:

Simplifying
x + y2 = 0

Solving
x + y2 = 0

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

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

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

Simplifying
x = -1y2

Subproblem 4
Set the factor '(x + -1y2)' equal to zero and attempt to solve:

Simplifying
x + -1y2 = 0

Solving
x + -1y2 = 0

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

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

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

Simplifying
x = y2
Solution
x = {-3y2, 3y2, -1y2, y2}

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