4x^3-2x^2y-12xy^2=0

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Solution for 4x^3-2x^2y-12xy^2=0 equation: 


Simplifying
4x3 + -2x2y + -12xy2 = 0

Reorder the terms:
-12xy2 + -2x2y + 4x3 = 0

Solving
-12xy2 + -2x2y + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6y2 + -1xy + 2x2) = 0

Factor a trinomial.
2x((-3y + -2x)(2y + -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 '(-3y + -2x)' equal to zero and attempt to solve:

Simplifying
-3y + -2x = 0

Reorder the terms:
-2x + -3y = 0

Solving
-2x + -3y = 0

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

Add '3y' to each side of the equation.
-2x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
-2x + 0 = 0 + 3y
-2x = 0 + 3y
Remove the zero:
-2x = 3y

Divide each side by '-2'.
x = -1.5y

Simplifying
x = -1.5y

Subproblem 3
Set the factor '(2y + -1x)' equal to zero and attempt to solve:

Simplifying
2y + -1x = 0

Reorder the terms:
-1x + 2y = 0

Solving
-1x + 2y = 0

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

Add '-2y' to each side of the equation.
-1x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x + 0 = 0 + -2y
-1x = 0 + -2y
Remove the zero:
-1x = -2y

Divide each side by '-1'.
x = 2y

Simplifying
x = 2y
Solution
x = {0, -1.5y, 2y}

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