(1-2x-3y)dx=(4x+6y)dy

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Solution for (1-2x-3y)dx=(4x+6y)dy equation: 


Simplifying
(1 + -2x + -3y) * dx = (4x + 6y) * dy

Reorder the terms for easier multiplication:
dx(1 + -2x + -3y) = (4x + 6y) * dy
(1 * dx + -2x * dx + -3y * dx) = (4x + 6y) * dy

Reorder the terms:
(1dx + -3dxy + -2dx2) = (4x + 6y) * dy
(1dx + -3dxy + -2dx2) = (4x + 6y) * dy

Reorder the terms for easier multiplication:
1dx + -3dxy + -2dx2 = dy(4x + 6y)
1dx + -3dxy + -2dx2 = (4x * dy + 6y * dy)
1dx + -3dxy + -2dx2 = (4dxy + 6dy2)

Solving
1dx + -3dxy + -2dx2 = 4dxy + 6dy2

Solving for variable 'd'.

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

Add '-4dxy' to each side of the equation.
1dx + -3dxy + -4dxy + -2dx2 = 4dxy + -4dxy + 6dy2

Combine like terms: -3dxy + -4dxy = -7dxy
1dx + -7dxy + -2dx2 = 4dxy + -4dxy + 6dy2

Combine like terms: 4dxy + -4dxy = 0
1dx + -7dxy + -2dx2 = 0 + 6dy2
1dx + -7dxy + -2dx2 = 6dy2

Add '-6dy2' to each side of the equation.
1dx + -7dxy + -2dx2 + -6dy2 = 6dy2 + -6dy2

Combine like terms: 6dy2 + -6dy2 = 0
1dx + -7dxy + -2dx2 + -6dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + -7xy + -2x2 + -6y2) = 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 '(x + -7xy + -2x2 + -6y2)' equal to zero and attempt to solve:

Simplifying
x + -7xy + -2x2 + -6y2 = 0

Solving
x + -7xy + -2x2 + -6y2 = 0

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

Add '-1x' to each side of the equation.
x + -7xy + -2x2 + -1x + -6y2 = 0 + -1x

Reorder the terms:
x + -1x + -7xy + -2x2 + -6y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + -7xy + -2x2 + -6y2 = 0 + -1x
-7xy + -2x2 + -6y2 = 0 + -1x
Remove the zero:
-7xy + -2x2 + -6y2 = -1x

Add '7xy' to each side of the equation.
-7xy + -2x2 + 7xy + -6y2 = -1x + 7xy

Reorder the terms:
-7xy + 7xy + -2x2 + -6y2 = -1x + 7xy

Combine like terms: -7xy + 7xy = 0
0 + -2x2 + -6y2 = -1x + 7xy
-2x2 + -6y2 = -1x + 7xy

Add '2x2' to each side of the equation.
-2x2 + 2x2 + -6y2 = -1x + 7xy + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + -6y2 = -1x + 7xy + 2x2
-6y2 = -1x + 7xy + 2x2

Add '6y2' to each side of the equation.
-6y2 + 6y2 = -1x + 7xy + 2x2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
0 = -1x + 7xy + 2x2 + 6y2

Simplifying
0 = -1x + 7xy + 2x2 + 6y2

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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