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

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


Simplifying
(5x + 4y) * dx + -1(4x + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(5x + 4y) + -1(4x + 4y) * dy = 0
(5x * dx + 4y * dx) + -1(4x + 4y) * dy = 0

Reorder the terms:
(4dxy + 5dx2) + -1(4x + 4y) * dy = 0
(4dxy + 5dx2) + -1(4x + 4y) * dy = 0

Reorder the terms for easier multiplication:
4dxy + 5dx2 + -1dy(4x + 4y) = 0
4dxy + 5dx2 + (4x * -1dy + 4y * -1dy) = 0
4dxy + 5dx2 + (-4dxy + -4dy2) = 0

Reorder the terms:
4dxy + -4dxy + 5dx2 + -4dy2 = 0

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

Solving
5dx2 + -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(5x2 + -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 '(5x2 + -4y2)' equal to zero and attempt to solve:

Simplifying
5x2 + -4y2 = 0

Solving
5x2 + -4y2 = 0

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

Add '-5x2' to each side of the equation.
5x2 + -5x2 + -4y2 = 0 + -5x2

Combine like terms: 5x2 + -5x2 = 0
0 + -4y2 = 0 + -5x2
-4y2 = 0 + -5x2
Remove the zero:
-4y2 = -5x2

Add '4y2' to each side of the equation.
-4y2 + 4y2 = -5x2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = -5x2 + 4y2

Simplifying
0 = -5x2 + 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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