(5v-u)du+(3v-7u)dv=0

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Solution for (5v-u)du+(3v-7u)dv=0 equation: 


Simplifying
(5v + -1u) * du + (3v + -7u) * dv = 0

Reorder the terms:
(-1u + 5v) * du + (3v + -7u) * dv = 0

Reorder the terms for easier multiplication:
du(-1u + 5v) + (3v + -7u) * dv = 0
(-1u * du + 5v * du) + (3v + -7u) * dv = 0

Reorder the terms:
(5duv + -1du2) + (3v + -7u) * dv = 0
(5duv + -1du2) + (3v + -7u) * dv = 0

Reorder the terms:
5duv + -1du2 + (-7u + 3v) * dv = 0

Reorder the terms for easier multiplication:
5duv + -1du2 + dv(-7u + 3v) = 0
5duv + -1du2 + (-7u * dv + 3v * dv) = 0
5duv + -1du2 + (-7duv + 3dv2) = 0

Reorder the terms:
5duv + -7duv + -1du2 + 3dv2 = 0

Combine like terms: 5duv + -7duv = -2duv
-2duv + -1du2 + 3dv2 = 0

Solving
-2duv + -1du2 + 3dv2 = 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(-2uv + -1u2 + 3v2) = 0

Factor a trinomial.
d((-1u + -3v)(u + -1v)) = 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 '(-1u + -3v)' equal to zero and attempt to solve:

Simplifying
-1u + -3v = 0

Solving
-1u + -3v = 0

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

Add 'u' to each side of the equation.
-1u + u + -3v = 0 + u

Combine like terms: -1u + u = 0
0 + -3v = 0 + u
-3v = 0 + u
Remove the zero:
-3v = u

Add '3v' to each side of the equation.
-3v + 3v = u + 3v

Combine like terms: -3v + 3v = 0
0 = u + 3v

Simplifying
0 = u + 3v

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(u + -1v)' equal to zero and attempt to solve:

Simplifying
u + -1v = 0

Solving
u + -1v = 0

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

Add '-1u' to each side of the equation.
u + -1u + -1v = 0 + -1u

Combine like terms: u + -1u = 0
0 + -1v = 0 + -1u
-1v = 0 + -1u
Remove the zero:
-1v = -1u

Add 'v' to each side of the equation.
-1v + v = -1u + v

Combine like terms: -1v + v = 0
0 = -1u + v

Simplifying
0 = -1u + v

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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