(6xy^4+5)dx+2(6x^2y^5+1)dy=0

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Solution for (6xy^4+5)dx+2(6x^2y^5+1)dy=0 equation: 


Simplifying
(6xy4 + 5) * dx + 2(6x2y5 + 1) * dy = 0

Reorder the terms:
(5 + 6xy4) * dx + 2(6x2y5 + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(5 + 6xy4) + 2(6x2y5 + 1) * dy = 0
(5 * dx + 6xy4 * dx) + 2(6x2y5 + 1) * dy = 0
(5dx + 6dx2y4) + 2(6x2y5 + 1) * dy = 0

Reorder the terms:
5dx + 6dx2y4 + 2(1 + 6x2y5) * dy = 0

Reorder the terms for easier multiplication:
5dx + 6dx2y4 + 2dy(1 + 6x2y5) = 0
5dx + 6dx2y4 + (1 * 2dy + 6x2y5 * 2dy) = 0

Reorder the terms:
5dx + 6dx2y4 + (12dx2y6 + 2dy) = 0
5dx + 6dx2y4 + (12dx2y6 + 2dy) = 0

Solving
5dx + 6dx2y4 + 12dx2y6 + 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(5x + 6x2y4 + 12x2y6 + 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 '(5x + 6x2y4 + 12x2y6 + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 6x2y4 + 12x2y6 + 2y = 0

Solving
5x + 6x2y4 + 12x2y6 + 2y = 0

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

Add '-5x' to each side of the equation.
5x + 6x2y4 + 12x2y6 + -5x + 2y = 0 + -5x

Reorder the terms:
5x + -5x + 6x2y4 + 12x2y6 + 2y = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 6x2y4 + 12x2y6 + 2y = 0 + -5x
6x2y4 + 12x2y6 + 2y = 0 + -5x
Remove the zero:
6x2y4 + 12x2y6 + 2y = -5x

Add '-6x2y4' to each side of the equation.
6x2y4 + 12x2y6 + -6x2y4 + 2y = -5x + -6x2y4

Reorder the terms:
6x2y4 + -6x2y4 + 12x2y6 + 2y = -5x + -6x2y4

Combine like terms: 6x2y4 + -6x2y4 = 0
0 + 12x2y6 + 2y = -5x + -6x2y4
12x2y6 + 2y = -5x + -6x2y4

Add '-12x2y6' to each side of the equation.
12x2y6 + -12x2y6 + 2y = -5x + -6x2y4 + -12x2y6

Combine like terms: 12x2y6 + -12x2y6 = 0
0 + 2y = -5x + -6x2y4 + -12x2y6
2y = -5x + -6x2y4 + -12x2y6

Add '-2y' to each side of the equation.
2y + -2y = -5x + -6x2y4 + -12x2y6 + -2y

Combine like terms: 2y + -2y = 0
0 = -5x + -6x2y4 + -12x2y6 + -2y

Simplifying
0 = -5x + -6x2y4 + -12x2y6 + -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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