9x^4-30x^2y^2+25y^4=0

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Solution for 9x^4-30x^2y^2+25y^4=0 equation: 


Simplifying
9x4 + -30x2y2 + 25y4 = 0

Reorder the terms:
-30x2y2 + 9x4 + 25y4 = 0

Solving
-30x2y2 + 9x4 + 25y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x2 + -5y2)(3x2 + -5y2) = 0


Subproblem 1
Set the factor '(3x2 + -5y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -5y2 = 0

Solving
3x2 + -5y2 = 0

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

Add '5y2' to each side of the equation.
3x2 + -5y2 + 5y2 = 0 + 5y2

Combine like terms: -5y2 + 5y2 = 0
3x2 + 0 = 0 + 5y2
3x2 = 0 + 5y2
Remove the zero:
3x2 = 5y2

Divide each side by '3'.
x2 = 1.666666667y2

Simplifying
x2 = 1.666666667y2

Take the square root of each side:
x = {-1.290994449y, 1.290994449y}

Subproblem 2
Set the factor '(3x2 + -5y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -5y2 = 0

Solving
3x2 + -5y2 = 0

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

Add '5y2' to each side of the equation.
3x2 + -5y2 + 5y2 = 0 + 5y2

Combine like terms: -5y2 + 5y2 = 0
3x2 + 0 = 0 + 5y2
3x2 = 0 + 5y2
Remove the zero:
3x2 = 5y2

Divide each side by '3'.
x2 = 1.666666667y2

Simplifying
x2 = 1.666666667y2

Take the square root of each side:
x = {-1.290994449y, 1.290994449y}
Solution
x = {-1.290994449y, 1.290994449y, -1.290994449y, 1.290994449y}

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