12x^3y-22x^2y^2+8xy^3=0

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Solution for 12x^3y-22x^2y^2+8xy^3=0 equation:


Simplifying
12x3y + -22x2y2 + 8xy3 = 0

Reorder the terms:
8xy3 + -22x2y2 + 12x3y = 0

Solving
8xy3 + -22x2y2 + 12x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(4y2 + -11xy + 6x2) = 0

Factor a trinomial.
2xy((y + -2x)(4y + -3x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 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 '(4y + -3x)' equal to zero and attempt to solve: Simplifying 4y + -3x = 0 Reorder the terms: -3x + 4y = 0 Solving -3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. -3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 -3x + 0 = 0 + -4y -3x = 0 + -4y Remove the zero: -3x = -4y Divide each side by '-3'. x = 1.333333333y Simplifying x = 1.333333333y

Solution

x = {0.5y, 1.333333333y}

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