(4y+3x-11)dx+(2x+y-5)dy=0

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Solution for (4y+3x-11)dx+(2x+y-5)dy=0 equation: 


Simplifying
(4y + 3x + -11) * dx + (2x + y + -5) * dy = 0

Reorder the terms:
(-11 + 3x + 4y) * dx + (2x + y + -5) * dy = 0

Reorder the terms for easier multiplication:
dx(-11 + 3x + 4y) + (2x + y + -5) * dy = 0
(-11 * dx + 3x * dx + 4y * dx) + (2x + y + -5) * dy = 0

Reorder the terms:
(-11dx + 4dxy + 3dx2) + (2x + y + -5) * dy = 0
(-11dx + 4dxy + 3dx2) + (2x + y + -5) * dy = 0

Reorder the terms:
-11dx + 4dxy + 3dx2 + (-5 + 2x + y) * dy = 0

Reorder the terms for easier multiplication:
-11dx + 4dxy + 3dx2 + dy(-5 + 2x + y) = 0
-11dx + 4dxy + 3dx2 + (-5 * dy + 2x * dy + y * dy) = 0

Reorder the terms:
-11dx + 4dxy + 3dx2 + (2dxy + -5dy + dy2) = 0
-11dx + 4dxy + 3dx2 + (2dxy + -5dy + dy2) = 0

Reorder the terms:
-11dx + 4dxy + 2dxy + 3dx2 + -5dy + dy2 = 0

Combine like terms: 4dxy + 2dxy = 6dxy
-11dx + 6dxy + 3dx2 + -5dy + dy2 = 0

Solving
-11dx + 6dxy + 3dx2 + -5dy + dy2 = 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(-11x + 6xy + 3x2 + -5y + y2) = 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 '(-11x + 6xy + 3x2 + -5y + y2)' equal to zero and attempt to solve:

Simplifying
-11x + 6xy + 3x2 + -5y + y2 = 0

Solving
-11x + 6xy + 3x2 + -5y + y2 = 0

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

Add '11x' to each side of the equation.
-11x + 6xy + 3x2 + -5y + 11x + y2 = 0 + 11x

Reorder the terms:
-11x + 11x + 6xy + 3x2 + -5y + y2 = 0 + 11x

Combine like terms: -11x + 11x = 0
0 + 6xy + 3x2 + -5y + y2 = 0 + 11x
6xy + 3x2 + -5y + y2 = 0 + 11x
Remove the zero:
6xy + 3x2 + -5y + y2 = 11x

Add '-6xy' to each side of the equation.
6xy + 3x2 + -5y + -6xy + y2 = 11x + -6xy

Reorder the terms:
6xy + -6xy + 3x2 + -5y + y2 = 11x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + 3x2 + -5y + y2 = 11x + -6xy
3x2 + -5y + y2 = 11x + -6xy

Add '-3x2' to each side of the equation.
3x2 + -5y + -3x2 + y2 = 11x + -6xy + -3x2

Reorder the terms:
3x2 + -3x2 + -5y + y2 = 11x + -6xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -5y + y2 = 11x + -6xy + -3x2
-5y + y2 = 11x + -6xy + -3x2

Add '5y' to each side of the equation.
-5y + 5y + y2 = 11x + -6xy + -3x2 + 5y

Combine like terms: -5y + 5y = 0
0 + y2 = 11x + -6xy + -3x2 + 5y
y2 = 11x + -6xy + -3x2 + 5y

Add '-1y2' to each side of the equation.
y2 + -1y2 = 11x + -6xy + -3x2 + 5y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = 11x + -6xy + -3x2 + 5y + -1y2

Simplifying
0 = 11x + -6xy + -3x2 + 5y + -1y2

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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