27xy^2-12x=0

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Solution for 27xy^2-12x=0 equation: 


Simplifying
27xy2 + -12x = 0

Reorder the terms:
-12x + 27xy2 = 0

Solving
-12x + 27xy2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + 9y2) = 0

Factor a difference between two squares.
3x((2 + 3y)(-2 + 3y)) = 0

Ignore the factor 3.

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 '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

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

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

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

Combine like terms: 3y + -3y = 0
0 = -2 + -3y

Simplifying
0 = -2 + -3y

The solution to this equation could not be determined.

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

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

Simplifying
-2 + 3y = 0

Solving
-2 + 3y = 0

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

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

Combine like terms: -2 + 2 = 0
0 + 3y = 0 + 2
3y = 0 + 2

Combine like terms: 0 + 2 = 2
3y = 2

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

Combine like terms: 3y + -3y = 0
0 = 2 + -3y

Simplifying
0 = 2 + -3y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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