(9x-7y)*dx+(7x+4y)*dy=0

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Solution for (9x-7y)*dx+(7x+4y)*dy=0 equation: 


Simplifying
(9x + -7y) * dx + (7x + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(9x + -7y) + (7x + 4y) * dy = 0
(9x * dx + -7y * dx) + (7x + 4y) * dy = 0

Reorder the terms:
(-7dxy + 9dx2) + (7x + 4y) * dy = 0
(-7dxy + 9dx2) + (7x + 4y) * dy = 0

Reorder the terms for easier multiplication:
-7dxy + 9dx2 + dy(7x + 4y) = 0
-7dxy + 9dx2 + (7x * dy + 4y * dy) = 0
-7dxy + 9dx2 + (7dxy + 4dy2) = 0

Reorder the terms:
-7dxy + 7dxy + 9dx2 + 4dy2 = 0

Combine like terms: -7dxy + 7dxy = 0
0 + 9dx2 + 4dy2 = 0
9dx2 + 4dy2 = 0

Solving
9dx2 + 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(9x2 + 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 '(9x2 + 4y2)' equal to zero and attempt to solve:

Simplifying
9x2 + 4y2 = 0

Solving
9x2 + 4y2 = 0

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

Add '-9x2' to each side of the equation.
9x2 + -9x2 + 4y2 = 0 + -9x2

Combine like terms: 9x2 + -9x2 = 0
0 + 4y2 = 0 + -9x2
4y2 = 0 + -9x2
Remove the zero:
4y2 = -9x2

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -9x2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -9x2 + -4y2

Simplifying
0 = -9x2 + -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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