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

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


Simplifying
(12xy + -3) * dx + (x2 + 4y) * dy = 0

Reorder the terms:
(-3 + 12xy) * dx + (x2 + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(-3 + 12xy) + (x2 + 4y) * dy = 0
(-3 * dx + 12xy * dx) + (x2 + 4y) * dy = 0
(-3dx + 12dx2y) + (x2 + 4y) * dy = 0

Reorder the terms for easier multiplication:
-3dx + 12dx2y + dy(x2 + 4y) = 0
-3dx + 12dx2y + (x2 * dy + 4y * dy) = 0
-3dx + 12dx2y + (dx2y + 4dy2) = 0

Combine like terms: 12dx2y + dx2y = 13dx2y
-3dx + 13dx2y + 4dy2 = 0

Solving
-3dx + 13dx2y + 4dy2 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(-3x + 13x2y + 4y2) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(-3x + 13x2y + 4y2)' equal to zero and attempt to solve:

Simplifying
-3x + 13x2y + 4y2 = 0

Solving
-3x + 13x2y + 4y2 = 0

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

Add '3x' to each side of the equation.
-3x + 13x2y + 3x + 4y2 = 0 + 3x

Reorder the terms:
-3x + 3x + 13x2y + 4y2 = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + 13x2y + 4y2 = 0 + 3x
13x2y + 4y2 = 0 + 3x
Remove the zero:
13x2y + 4y2 = 3x

Add '-13x2y' to each side of the equation.
13x2y + -13x2y + 4y2 = 3x + -13x2y

Combine like terms: 13x2y + -13x2y = 0
0 + 4y2 = 3x + -13x2y
4y2 = 3x + -13x2y

Add '-4y2' to each side of the equation.
4y2 + -4y2 = 3x + -13x2y + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = 3x + -13x2y + -4y2

Simplifying
0 = 3x + -13x2y + -4y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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