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

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


Simplifying
(12x3y2) + -1(3xy4) = 0

Remove parenthesis around (3xy4)
(12x3y2) + -1 * 3xy4 = 0

Multiply -1 * 3
(12x3y2) + -3xy4 = 0

Reorder the terms:
-3xy4 + (12x3y2) = 0

Solving
-3xy4 + (12x3y2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy2'.
3xy2(-1y2 + (4x2)) = 0

Factor a difference between two squares.
3xy2((y + (2x))(-1y + (2x))) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve:

Simplifying
xy2 = 0

Solving
xy2 = 0

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

Simplifying
xy2 = 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 '(y + (2x))' equal to zero and attempt to solve:

Simplifying
y + (2x) = 0

Reorder the terms:
(2x) + y = 0

Solving
(2x) + y = 0

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

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

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

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y

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

Simplifying
-1y + (2x) = 0

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

Solving
(2x) + -1y = 0

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

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

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

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {-0.5y, 0.5y}

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