-dY(3X-7Y)-(3Y-7X)dX=0

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Solution for -dY(3X-7Y)-(3Y-7X)dX=0 equation: 


Simplifying
-1dY(3X + -7Y) + -1(3Y + -7X) * dX = 0
(3X * -1dY + -7Y * -1dY) + -1(3Y + -7X) * dX = 0
(-3dXY + 7dY2) + -1(3Y + -7X) * dX = 0

Reorder the terms:
-3dXY + 7dY2 + -1(-7X + 3Y) * dX = 0

Reorder the terms for easier multiplication:
-3dXY + 7dY2 + -1dX(-7X + 3Y) = 0
-3dXY + 7dY2 + (-7X * -1dX + 3Y * -1dX) = 0

Reorder the terms:
-3dXY + 7dY2 + (-3dXY + 7dX2) = 0
-3dXY + 7dY2 + (-3dXY + 7dX2) = 0

Reorder the terms:
-3dXY + -3dXY + 7dX2 + 7dY2 = 0

Combine like terms: -3dXY + -3dXY = -6dXY
-6dXY + 7dX2 + 7dY2 = 0

Solving
-6dXY + 7dX2 + 7dY2 = 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(-6XY + 7X2 + 7Y2) = 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 '(-6XY + 7X2 + 7Y2)' equal to zero and attempt to solve:

Simplifying
-6XY + 7X2 + 7Y2 = 0

Solving
-6XY + 7X2 + 7Y2 = 0

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

Add '6XY' to each side of the equation.
-6XY + 7X2 + 6XY + 7Y2 = 0 + 6XY

Reorder the terms:
-6XY + 6XY + 7X2 + 7Y2 = 0 + 6XY

Combine like terms: -6XY + 6XY = 0
0 + 7X2 + 7Y2 = 0 + 6XY
7X2 + 7Y2 = 0 + 6XY
Remove the zero:
7X2 + 7Y2 = 6XY

Add '-7X2' to each side of the equation.
7X2 + -7X2 + 7Y2 = 6XY + -7X2

Combine like terms: 7X2 + -7X2 = 0
0 + 7Y2 = 6XY + -7X2
7Y2 = 6XY + -7X2

Add '-7Y2' to each side of the equation.
7Y2 + -7Y2 = 6XY + -7X2 + -7Y2

Combine like terms: 7Y2 + -7Y2 = 0
0 = 6XY + -7X2 + -7Y2

Simplifying
0 = 6XY + -7X2 + -7Y2

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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