12x^3+8x^2y-20xy^2=0

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Solution for 12x^3+8x^2y-20xy^2=0 equation: 


Simplifying
12x3 + 8x2y + -20xy2 = 0

Reorder the terms:
-20xy2 + 8x2y + 12x3 = 0

Solving
-20xy2 + 8x2y + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-5y2 + 2xy + 3x2) = 0

Factor a trinomial.
4x((-5y + -3x)(y + -1x)) = 0

Ignore the factor 4.

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 '(-5y + -3x)' equal to zero and attempt to solve:

Simplifying
-5y + -3x = 0

Reorder the terms:
-3x + -5y = 0

Solving
-3x + -5y = 0

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

Add '5y' to each side of the equation.
-3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-3x + 0 = 0 + 5y
-3x = 0 + 5y
Remove the zero:
-3x = 5y

Divide each side by '-3'.
x = -1.666666667y

Simplifying
x = -1.666666667y

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

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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

Simplifying
x = y
Solution
x = {0, -1.666666667y, y}

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