64x^4-100x^2y^2=0

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Solution for 64x^4-100x^2y^2=0 equation: 


Simplifying
64x4 + -100x2y2 = 0

Reorder the terms:
-100x2y2 + 64x4 = 0

Solving
-100x2y2 + 64x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-25y2 + 16x2) = 0

Factor a difference between two squares.
4x2((5y + 4x)(-5y + 4x)) = 0

Ignore the factor 4.

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 + 4x)' equal to zero and attempt to solve:

Simplifying
5y + 4x = 0

Reorder the terms:
4x + 5y = 0

Solving
4x + 5y = 0

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

Add '-5y' to each side of the equation.
4x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
4x + 0 = 0 + -5y
4x = 0 + -5y
Remove the zero:
4x = -5y

Divide each side by '4'.
x = -1.25y

Simplifying
x = -1.25y

Subproblem 3
Set the factor '(-5y + 4x)' equal to zero and attempt to solve:

Simplifying
-5y + 4x = 0

Reorder the terms:
4x + -5y = 0

Solving
4x + -5y = 0

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

Add '5y' to each side of the equation.
4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4x + 0 = 0 + 5y
4x = 0 + 5y
Remove the zero:
4x = 5y

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y
Solution
x = {0, -1.25y, 1.25y}

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