9(y-1)dy+(x-3)dx=0

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Solution for 9(y-1)dy+(x-3)dx=0 equation: 


Simplifying
9(y + -1) * dy + (x + -3) * dx = 0

Reorder the terms:
9(-1 + y) * dy + (x + -3) * dx = 0

Reorder the terms for easier multiplication:
9dy(-1 + y) + (x + -3) * dx = 0
(-1 * 9dy + y * 9dy) + (x + -3) * dx = 0
(-9dy + 9dy2) + (x + -3) * dx = 0

Reorder the terms:
-9dy + 9dy2 + (-3 + x) * dx = 0

Reorder the terms for easier multiplication:
-9dy + 9dy2 + dx(-3 + x) = 0
-9dy + 9dy2 + (-3 * dx + x * dx) = 0
-9dy + 9dy2 + (-3dx + dx2) = 0

Reorder the terms:
-3dx + dx2 + -9dy + 9dy2 = 0

Solving
-3dx + dx2 + -9dy + 9dy2 = 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(-3x + x2 + -9y + 9y2) = 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 '(-3x + x2 + -9y + 9y2)' equal to zero and attempt to solve:

Simplifying
-3x + x2 + -9y + 9y2 = 0

Solving
-3x + x2 + -9y + 9y2 = 0

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

Add '3x' to each side of the equation.
-3x + x2 + -9y + 3x + 9y2 = 0 + 3x

Reorder the terms:
-3x + 3x + x2 + -9y + 9y2 = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + x2 + -9y + 9y2 = 0 + 3x
x2 + -9y + 9y2 = 0 + 3x
Remove the zero:
x2 + -9y + 9y2 = 3x

Add '-1x2' to each side of the equation.
x2 + -9y + -1x2 + 9y2 = 3x + -1x2

Reorder the terms:
x2 + -1x2 + -9y + 9y2 = 3x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -9y + 9y2 = 3x + -1x2
-9y + 9y2 = 3x + -1x2

Add '9y' to each side of the equation.
-9y + 9y + 9y2 = 3x + -1x2 + 9y

Combine like terms: -9y + 9y = 0
0 + 9y2 = 3x + -1x2 + 9y
9y2 = 3x + -1x2 + 9y

Add '-9y2' to each side of the equation.
9y2 + -9y2 = 3x + -1x2 + 9y + -9y2

Combine like terms: 9y2 + -9y2 = 0
0 = 3x + -1x2 + 9y + -9y2

Simplifying
0 = 3x + -1x2 + 9y + -9y2

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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