5x^4-25x^3y-250y^2x^2=0

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Solution for 5x^4-25x^3y-250y^2x^2=0 equation: 


Simplifying
5x4 + -25x3y + -250y2x2 = 0

Reorder the terms:
-250x2y2 + -25x3y + 5x4 = 0

Solving
-250x2y2 + -25x3y + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(-50y2 + -5xy + x2) = 0

Factor a trinomial.
5x2((-5y + -1x)(10y + -1x)) = 0

Ignore the factor 5.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
-5y + -1x = 0

Reorder the terms:
-1x + -5y = 0

Solving
-1x + -5y = 0

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

Add '5y' to each side of the equation.
-1x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-1x + 0 = 0 + 5y
-1x = 0 + 5y
Remove the zero:
-1x = 5y

Divide each side by '-1'.
x = -5y

Simplifying
x = -5y

Subproblem 3
Set the factor '(10y + -1x)' equal to zero and attempt to solve:

Simplifying
10y + -1x = 0

Reorder the terms:
-1x + 10y = 0

Solving
-1x + 10y = 0

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

Add '-10y' to each side of the equation.
-1x + 10y + -10y = 0 + -10y

Combine like terms: 10y + -10y = 0
-1x + 0 = 0 + -10y
-1x = 0 + -10y
Remove the zero:
-1x = -10y

Divide each side by '-1'.
x = 10y

Simplifying
x = 10y
Solution
x = {0, -5y, 10y}

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