24x^2y-14xy^2+2y^3=0

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Solution for 24x^2y-14xy^2+2y^3=0 equation:


Simplifying
24x2y + -14xy2 + 2y3 = 0

Reorder the terms:
-14xy2 + 24x2y + 2y3 = 0

Solving
-14xy2 + 24x2y + 2y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-7xy + 12x2 + y2) = 0

Factor a trinomial.
2y((3x + -1y)(4x + -1y)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y 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 '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333y

Subproblem 3

Set the factor '(4x + -1y)' equal to zero and attempt to solve: Simplifying 4x + -1y = 0 Solving 4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 4x + 0 = 0 + y 4x = 0 + y Remove the zero: 4x = y Divide each side by '4'. x = 0.25y Simplifying x = 0.25y

Solution

x = {0.3333333333y, 0.25y}

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