(6xy+7)dx+(3x^2-2)dy=0

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Solution for (6xy+7)dx+(3x^2-2)dy=0 equation: 


Simplifying
(6xy + 7) * dx + (3x2 + -2) * dy = 0

Reorder the terms:
(7 + 6xy) * dx + (3x2 + -2) * dy = 0

Reorder the terms for easier multiplication:
dx(7 + 6xy) + (3x2 + -2) * dy = 0
(7 * dx + 6xy * dx) + (3x2 + -2) * dy = 0
(7dx + 6dx2y) + (3x2 + -2) * dy = 0

Reorder the terms:
7dx + 6dx2y + (-2 + 3x2) * dy = 0

Reorder the terms for easier multiplication:
7dx + 6dx2y + dy(-2 + 3x2) = 0
7dx + 6dx2y + (-2 * dy + 3x2 * dy) = 0

Reorder the terms:
7dx + 6dx2y + (3dx2y + -2dy) = 0
7dx + 6dx2y + (3dx2y + -2dy) = 0

Combine like terms: 6dx2y + 3dx2y = 9dx2y
7dx + 9dx2y + -2dy = 0

Solving
7dx + 9dx2y + -2dy = 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(7x + 9x2y + -2y) = 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 '(7x + 9x2y + -2y)' equal to zero and attempt to solve:

Simplifying
7x + 9x2y + -2y = 0

Solving
7x + 9x2y + -2y = 0

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

Add '-7x' to each side of the equation.
7x + 9x2y + -7x + -2y = 0 + -7x

Reorder the terms:
7x + -7x + 9x2y + -2y = 0 + -7x

Combine like terms: 7x + -7x = 0
0 + 9x2y + -2y = 0 + -7x
9x2y + -2y = 0 + -7x
Remove the zero:
9x2y + -2y = -7x

Add '-9x2y' to each side of the equation.
9x2y + -9x2y + -2y = -7x + -9x2y

Combine like terms: 9x2y + -9x2y = 0
0 + -2y = -7x + -9x2y
-2y = -7x + -9x2y

Add '2y' to each side of the equation.
-2y + 2y = -7x + -9x2y + 2y

Combine like terms: -2y + 2y = 0
0 = -7x + -9x2y + 2y

Simplifying
0 = -7x + -9x2y + 2y

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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