12x^3y^2-24x^2y^3+16x^2y^4=0

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Solution for 12x^3y^2-24x^2y^3+16x^2y^4=0 equation: 


Simplifying
12x3y2 + -24x2y3 + 16x2y4 = 0

Reorder the terms:
-24x2y3 + 16x2y4 + 12x3y2 = 0

Solving
-24x2y3 + 16x2y4 + 12x3y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2y2'.
4x2y2(-6y + 4y2 + 3x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2y2' equal to zero and attempt to solve:

Simplifying
x2y2 = 0

Solving
x2y2 = 0

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

Simplifying
x2y2 = 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 '(-6y + 4y2 + 3x)' equal to zero and attempt to solve:

Simplifying
-6y + 4y2 + 3x = 0

Reorder the terms:
3x + -6y + 4y2 = 0

Solving
3x + -6y + 4y2 = 0

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

Add '6y' to each side of the equation.
3x + -6y + 6y + 4y2 = 0 + 6y

Combine like terms: -6y + 6y = 0
3x + 0 + 4y2 = 0 + 6y
3x + 4y2 = 0 + 6y
Remove the zero:
3x + 4y2 = 6y

Add '-4y2' to each side of the equation.
3x + 4y2 + -4y2 = 6y + -4y2

Combine like terms: 4y2 + -4y2 = 0
3x + 0 = 6y + -4y2
3x = 6y + -4y2

Divide each side by '3'.
x = 2y + -1.333333333y2

Simplifying
x = 2y + -1.333333333y2
Solution
x = {2y + -1.333333333y2}

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