(4x+6y)dy=(4x+2y)dx

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


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

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

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

Reorder the terms:
4dxy + 6dy2 = (2dxy + 4dx2)
4dxy + 6dy2 = (2dxy + 4dx2)

Solving
4dxy + 6dy2 = 2dxy + 4dx2

Solving for variable 'd'.

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

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

Combine like terms: 4dxy + -2dxy = 2dxy
2dxy + 6dy2 = 2dxy + -2dxy + 4dx2

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

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

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

Factor out the Greatest Common Factor (GCF), '2d'.
2d(xy + -2x2 + 3y2) = 0

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

Ignore the factor 2.

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 '(-1x + -1y)' equal to zero and attempt to solve:

Simplifying
-1x + -1y = 0

Solving
-1x + -1y = 0

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

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

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

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

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

Simplifying
0 = x + 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 '(2x + -3y)' equal to zero and attempt to solve:

Simplifying
2x + -3y = 0

Solving
2x + -3y = 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 + -3y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -3y = 0 + -2x
-3y = 0 + -2x
Remove the zero:
-3y = -2x

Add '3y' to each side of the equation.
-3y + 3y = -2x + 3y

Combine like terms: -3y + 3y = 0
0 = -2x + 3y

Simplifying
0 = -2x + 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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