4x^4y+16x^3y^2-84x^2y^3=0

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Solution for 4x^4y+16x^3y^2-84x^2y^3=0 equation: 


Simplifying
4x4y + 16x3y2 + -84x2y3 = 0

Reorder the terms:
-84x2y3 + 16x3y2 + 4x4y = 0

Solving
-84x2y3 + 16x3y2 + 4x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2y'.
4x2y(-21y2 + 4xy + x2) = 0

Factor a trinomial.
4x2y((-7y + -1x)(3y + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(-7y + -1x)' equal to zero and attempt to solve:

Simplifying
-7y + -1x = 0

Reorder the terms:
-1x + -7y = 0

Solving
-1x + -7y = 0

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

Add '7y' to each side of the equation.
-1x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
-1x + 0 = 0 + 7y
-1x = 0 + 7y
Remove the zero:
-1x = 7y

Divide each side by '-1'.
x = -7y

Simplifying
x = -7y

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

Simplifying
3y + -1x = 0

Reorder the terms:
-1x + 3y = 0

Solving
-1x + 3y = 0

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

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

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

Divide each side by '-1'.
x = 3y

Simplifying
x = 3y
Solution
x = {-7y, 3y}

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