2x^6y^4-42x^5y^5+216x^4y^6=

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Solution for 2x^6y^4-42x^5y^5+216x^4y^6= equation: 


Simplifying
2x6y4 + -42x5y5 + 216x4y6 = 0

Reorder the terms:
216x4y6 + -42x5y5 + 2x6y4 = 0

Solving
216x4y6 + -42x5y5 + 2x6y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x4y4'.
2x4y4(108y2 + -21xy + x2) = 0

Factor a trinomial.
2x4y4((9y + -1x)(12y + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x4y4' equal to zero and attempt to solve:

Simplifying
x4y4 = 0

Solving
x4y4 = 0

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

Simplifying
x4y4 = 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 '(9y + -1x)' equal to zero and attempt to solve:

Simplifying
9y + -1x = 0

Reorder the terms:
-1x + 9y = 0

Solving
-1x + 9y = 0

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

Add '-9y' to each side of the equation.
-1x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
-1x + 0 = 0 + -9y
-1x = 0 + -9y
Remove the zero:
-1x = -9y

Divide each side by '-1'.
x = 9y

Simplifying
x = 9y

Subproblem 3
Set the factor '(12y + -1x)' equal to zero and attempt to solve:

Simplifying
12y + -1x = 0

Reorder the terms:
-1x + 12y = 0

Solving
-1x + 12y = 0

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

Add '-12y' to each side of the equation.
-1x + 12y + -12y = 0 + -12y

Combine like terms: 12y + -12y = 0
-1x + 0 = 0 + -12y
-1x = 0 + -12y
Remove the zero:
-1x = -12y

Divide each side by '-1'.
x = 12y

Simplifying
x = 12y
Solution
x = {9y, 12y}

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