left(5y+4xright)dx+left(2x+yright)dy=0

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Solution for left(5y+4xright)dx+left(2x+yright)dy=0 equation: 


Simplifying
left(5y + 4xright) * dx + left(2x + yright) * dy = 0

Reorder the terms:
eflt(4ghirtx + 5y) * dx + left(2x + yright) * dy = 0

Reorder the terms for easier multiplication:
eflt * dx(4ghirtx + 5y) + left(2x + yright) * dy = 0

Multiply eflt * dx
defltx(4ghirtx + 5y) + left(2x + yright) * dy = 0
(4ghirtx * defltx + 5y * defltx) + left(2x + yright) * dy = 0
(4defghilrt2x2 + 5defltxy) + left(2x + yright) * dy = 0

Reorder the terms:
4defghilrt2x2 + 5defltxy + eflt(ghirty + 2x) * dy = 0

Reorder the terms for easier multiplication:
4defghilrt2x2 + 5defltxy + eflt * dy(ghirty + 2x) = 0

Multiply eflt * dy
4defghilrt2x2 + 5defltxy + deflty(ghirty + 2x) = 0
4defghilrt2x2 + 5defltxy + (ghirty * deflty + 2x * deflty) = 0
4defghilrt2x2 + 5defltxy + (defghilrt2y2 + 2defltxy) = 0

Reorder the terms:
4defghilrt2x2 + defghilrt2y2 + 5defltxy + 2defltxy = 0

Combine like terms: 5defltxy + 2defltxy = 7defltxy
4defghilrt2x2 + defghilrt2y2 + 7defltxy = 0

Solving
4defghilrt2x2 + defghilrt2y2 + 7defltxy = 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), 'deflt'.
deflt(4ghirtx2 + ghirty2 + 7xy) = 0


Subproblem 1
Set the factor 'deflt' equal to zero and attempt to solve:

Simplifying
deflt = 0

Solving
deflt = 0

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

Simplifying
deflt = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(4ghirtx2 + ghirty2 + 7xy)' equal to zero and attempt to solve:

Simplifying
4ghirtx2 + ghirty2 + 7xy = 0

Solving
4ghirtx2 + ghirty2 + 7xy = 0

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

Add '-4ghirtx2' to each side of the equation.
4ghirtx2 + ghirty2 + -4ghirtx2 + 7xy = 0 + -4ghirtx2

Reorder the terms:
4ghirtx2 + -4ghirtx2 + ghirty2 + 7xy = 0 + -4ghirtx2

Combine like terms: 4ghirtx2 + -4ghirtx2 = 0
0 + ghirty2 + 7xy = 0 + -4ghirtx2
ghirty2 + 7xy = 0 + -4ghirtx2
Remove the zero:
ghirty2 + 7xy = -4ghirtx2

Add '-1ghirty2' to each side of the equation.
ghirty2 + -1ghirty2 + 7xy = -4ghirtx2 + -1ghirty2

Combine like terms: ghirty2 + -1ghirty2 = 0
0 + 7xy = -4ghirtx2 + -1ghirty2
7xy = -4ghirtx2 + -1ghirty2

Add '-7xy' to each side of the equation.
7xy + -7xy = -4ghirtx2 + -1ghirty2 + -7xy

Combine like terms: 7xy + -7xy = 0
0 = -4ghirtx2 + -1ghirty2 + -7xy

Simplifying
0 = -4ghirtx2 + -1ghirty2 + -7xy

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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