2x^3-10x^2y-12y^2x=0

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Solution for 2x^3-10x^2y-12y^2x=0 equation: 


Simplifying
2x3 + -10x2y + -12y2x = 0

Reorder the terms:
-12xy2 + -10x2y + 2x3 = 0

Solving
-12xy2 + -10x2y + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6y2 + -5xy + x2) = 0

Factor a trinomial.
2x((-1y + -1x)(6y + -1x)) = 0

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1y + -1x)' equal to zero and attempt to solve:

Simplifying
-1y + -1x = 0

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

Solving
-1x + -1y = 0

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

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

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

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

Simplifying
x = -1y

Subproblem 3
Set the factor '(6y + -1x)' equal to zero and attempt to solve:

Simplifying
6y + -1x = 0

Reorder the terms:
-1x + 6y = 0

Solving
-1x + 6y = 0

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

Add '-6y' to each side of the equation.
-1x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
-1x + 0 = 0 + -6y
-1x = 0 + -6y
Remove the zero:
-1x = -6y

Divide each side by '-1'.
x = 6y

Simplifying
x = 6y
Solution
x = {0, -1y, 6y}

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