2x^4-13x^2y^2-45y^4=

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Solution for 2x^4-13x^2y^2-45y^4= equation: 


Simplifying
2x4 + -13x2y2 + -45y4 = 0

Reorder the terms:
-13x2y2 + 2x4 + -45y4 = 0

Solving
-13x2y2 + 2x4 + -45y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -9y2)(2x2 + 5y2) = 0

Factor a difference between two squares.
((x + 3y)(x + -3y))(2x2 + 5y2) = 0


Subproblem 1
Set the factor '(2x2 + 5y2)' equal to zero and attempt to solve:

Simplifying
2x2 + 5y2 = 0

Solving
2x2 + 5y2 = 0

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

Add '-5y2' to each side of the equation.
2x2 + 5y2 + -5y2 = 0 + -5y2

Combine like terms: 5y2 + -5y2 = 0
2x2 + 0 = 0 + -5y2
2x2 = 0 + -5y2
Remove the zero:
2x2 = -5y2

Divide each side by '2'.
x2 = -2.5y2

Simplifying
x2 = -2.5y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y

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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

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

Simplifying
x = 3y
Solution
x = {-3y, 3y}

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