x^5+4x^4y-5x^3y^2=0

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


Simplifying
x5 + 4x4y + -5x3y2 = 0

Reorder the terms:
-5x3y2 + 4x4y + x5 = 0

Solving
-5x3y2 + 4x4y + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-5y2 + 4xy + x2) = 0

Factor a trinomial.
x3((-5y + -1x)(y + -1x)) = 0


Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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

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

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