6x^2y^4-54x^4=0

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Solution for 6x^2y^4-54x^4=0 equation: 


Simplifying
6x2y4 + -54x4 = 0

Solving
6x2y4 + -54x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(y4 + -9x2) = 0

Factor a difference between two squares.
6x2((y2 + 3x)(y2 + -3x)) = 0

Ignore the factor 6.

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 '(y2 + 3x)' equal to zero and attempt to solve:

Simplifying
y2 + 3x = 0

Reorder the terms:
3x + y2 = 0

Solving
3x + y2 = 0

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

Add '-1y2' to each side of the equation.
3x + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
3x + 0 = 0 + -1y2
3x = 0 + -1y2
Remove the zero:
3x = -1y2

Divide each side by '3'.
x = -0.3333333333y2

Simplifying
x = -0.3333333333y2

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

Simplifying
y2 + -3x = 0

Reorder the terms:
-3x + y2 = 0

Solving
-3x + y2 = 0

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

Add '-1y2' to each side of the equation.
-3x + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
-3x + 0 = 0 + -1y2
-3x = 0 + -1y2
Remove the zero:
-3x = -1y2

Divide each side by '-3'.
x = 0.3333333333y2

Simplifying
x = 0.3333333333y2
Solution
x = {0, -0.3333333333y2, 0.3333333333y2}

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