(4x^3y^3-2xy)dx+(3x^4y^2-x^2)oly=0

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


Simplifying
(4x3y3 + -2xy) * dx + (3x4y2 + -1x2) * oly = 0

Reorder the terms:
(-2xy + 4x3y3) * dx + (3x4y2 + -1x2) * oly = 0

Reorder the terms for easier multiplication:
dx(-2xy + 4x3y3) + (3x4y2 + -1x2) * oly = 0
(-2xy * dx + 4x3y3 * dx) + (3x4y2 + -1x2) * oly = 0
(-2dx2y + 4dx4y3) + (3x4y2 + -1x2) * oly = 0

Reorder the terms:
-2dx2y + 4dx4y3 + (-1x2 + 3x4y2) * oly = 0

Reorder the terms for easier multiplication:
-2dx2y + 4dx4y3 + loy(-1x2 + 3x4y2) = 0
-2dx2y + 4dx4y3 + (-1x2 * loy + 3x4y2 * loy) = 0
-2dx2y + 4dx4y3 + (-1lox2y + 3lox4y3) = 0

Solving
-2dx2y + 4dx4y3 + -1lox2y + 3lox4y3 = 0

Solving for variable 'd'.

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

Add 'lox2y' to each side of the equation.
-2dx2y + 4dx4y3 + -1lox2y + lox2y + 3lox4y3 = 0 + lox2y

Combine like terms: -1lox2y + lox2y = 0
-2dx2y + 4dx4y3 + 0 + 3lox4y3 = 0 + lox2y
-2dx2y + 4dx4y3 + 3lox4y3 = 0 + lox2y
Remove the zero:
-2dx2y + 4dx4y3 + 3lox4y3 = lox2y

Add '-3lox4y3' to each side of the equation.
-2dx2y + 4dx4y3 + 3lox4y3 + -3lox4y3 = lox2y + -3lox4y3

Combine like terms: 3lox4y3 + -3lox4y3 = 0
-2dx2y + 4dx4y3 + 0 = lox2y + -3lox4y3
-2dx2y + 4dx4y3 = lox2y + -3lox4y3

Reorder the terms:
-2dx2y + 4dx4y3 + -1lox2y + 3lox4y3 = lox2y + -1lox2y + -3lox4y3 + 3lox4y3

Combine like terms: lox2y + -1lox2y = 0
-2dx2y + 4dx4y3 + -1lox2y + 3lox4y3 = 0 + -3lox4y3 + 3lox4y3
-2dx2y + 4dx4y3 + -1lox2y + 3lox4y3 = -3lox4y3 + 3lox4y3

Combine like terms: -3lox4y3 + 3lox4y3 = 0
-2dx2y + 4dx4y3 + -1lox2y + 3lox4y3 = 0

Factor out the Greatest Common Factor (GCF), 'x2y'.
x2y(-2d + 4dx2y2 + -1lo + 3lox2y2) = 0

Subproblem 1

Set the factor 'x2y' equal to zero and attempt to solve: Simplifying x2y = 0 Solving x2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2y' to each side of the equation. x2y + -1x2y = 0 + -1x2y Remove the zero: 0 = -1x2y Simplifying 0 = -1x2y 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 '(-2d + 4dx2y2 + -1lo + 3lox2y2)' equal to zero and attempt to solve: Simplifying -2d + 4dx2y2 + -1lo + 3lox2y2 = 0 Solving -2d + 4dx2y2 + -1lo + 3lox2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'lo' to each side of the equation. -2d + 4dx2y2 + -1lo + lo + 3lox2y2 = 0 + lo Combine like terms: -1lo + lo = 0 -2d + 4dx2y2 + 0 + 3lox2y2 = 0 + lo -2d + 4dx2y2 + 3lox2y2 = 0 + lo Remove the zero: -2d + 4dx2y2 + 3lox2y2 = lo Add '-3lox2y2' to each side of the equation. -2d + 4dx2y2 + 3lox2y2 + -3lox2y2 = lo + -3lox2y2 Combine like terms: 3lox2y2 + -3lox2y2 = 0 -2d + 4dx2y2 + 0 = lo + -3lox2y2 -2d + 4dx2y2 = lo + -3lox2y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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