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

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


Simplifying
(4x + 3y) * dy + (y + -2x) * dx = 0

Reorder the terms for easier multiplication:
dy(4x + 3y) + (y + -2x) * dx = 0
(4x * dy + 3y * dy) + (y + -2x) * dx = 0
(4dxy + 3dy2) + (y + -2x) * dx = 0

Reorder the terms:
4dxy + 3dy2 + (-2x + y) * dx = 0

Reorder the terms for easier multiplication:
4dxy + 3dy2 + dx(-2x + y) = 0
4dxy + 3dy2 + (-2x * dx + y * dx) = 0

Reorder the terms:
4dxy + 3dy2 + (dxy + -2dx2) = 0
4dxy + 3dy2 + (dxy + -2dx2) = 0

Reorder the terms:
4dxy + dxy + -2dx2 + 3dy2 = 0

Combine like terms: 4dxy + dxy = 5dxy
5dxy + -2dx2 + 3dy2 = 0

Solving
5dxy + -2dx2 + 3dy2 = 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(5xy + -2x2 + 3y2) = 0

Factor a trinomial.
d((-2x + -1y)(x + -3y)) = 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 '(-2x + -1y)' equal to zero and attempt to solve:

Simplifying
-2x + -1y = 0

Solving
-2x + -1y = 0

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

Add '2x' to each side of the equation.
-2x + 2x + -1y = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + -1y = 0 + 2x
-1y = 0 + 2x
Remove the zero:
-1y = 2x

Add 'y' to each side of the equation.
-1y + y = 2x + y

Combine like terms: -1y + y = 0
0 = 2x + y

Simplifying
0 = 2x + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -3y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -3y = 0 + -1x
-3y = 0 + -1x
Remove the zero:
-3y = -1x

Add '3y' to each side of the equation.
-3y + 3y = -1x + 3y

Combine like terms: -3y + 3y = 0
0 = -1x + 3y

Simplifying
0 = -1x + 3y

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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