36x^4-225x^2y^2=0

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Solution for 36x^4-225x^2y^2=0 equation: 


Simplifying
36x4 + -225x2y2 = 0

Reorder the terms:
-225x2y2 + 36x4 = 0

Solving
-225x2y2 + 36x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x2'.
9x2(-25y2 + 4x2) = 0

Factor a difference between two squares.
9x2((5y + 2x)(-5y + 2x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(5y + 2x)' equal to zero and attempt to solve:

Simplifying
5y + 2x = 0

Reorder the terms:
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y

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

Simplifying
-5y + 2x = 0

Reorder the terms:
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y
Solution
x = {0, -2.5y, 2.5y}

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