18x^4-8x^2y^2=0

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Solution for 18x^4-8x^2y^2=0 equation: 


Simplifying
18x4 + -8x2y2 = 0

Reorder the terms:
-8x2y2 + 18x4 = 0

Solving
-8x2y2 + 18x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-4y2 + 9x2) = 0

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

Ignore the factor 2.

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 '(2y + 3x)' equal to zero and attempt to solve:

Simplifying
2y + 3x = 0

Reorder the terms:
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

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

Simplifying
-2y + 3x = 0

Reorder the terms:
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Solution
x = {0, -0.6666666667y, 0.6666666667y}

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