3dy=(4x+5)dx

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Solution for 3dy=(4x+5)dx equation: 


Simplifying
3dy = (4x + 5) * dx

Reorder the terms:
3dy = (5 + 4x) * dx

Reorder the terms for easier multiplication:
3dy = dx(5 + 4x)
3dy = (5 * dx + 4x * dx)
3dy = (5dx + 4dx2)

Solving
3dy = 5dx + 4dx2

Solving for variable 'd'.

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

Add '-5dx' to each side of the equation.
-5dx + 3dy = 5dx + -5dx + 4dx2

Combine like terms: 5dx + -5dx = 0
-5dx + 3dy = 0 + 4dx2
-5dx + 3dy = 4dx2

Add '-4dx2' to each side of the equation.
-5dx + -4dx2 + 3dy = 4dx2 + -4dx2

Combine like terms: 4dx2 + -4dx2 = 0
-5dx + -4dx2 + 3dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-5x + -4x2 + 3y) = 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 + -4x2 + 3y)' equal to zero and attempt to solve:

Simplifying
-5x + -4x2 + 3y = 0

Solving
-5x + -4x2 + 3y = 0

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

Add '5x' to each side of the equation.
-5x + -4x2 + 5x + 3y = 0 + 5x

Reorder the terms:
-5x + 5x + -4x2 + 3y = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + -4x2 + 3y = 0 + 5x
-4x2 + 3y = 0 + 5x
Remove the zero:
-4x2 + 3y = 5x

Add '4x2' to each side of the equation.
-4x2 + 4x2 + 3y = 5x + 4x2

Combine like terms: -4x2 + 4x2 = 0
0 + 3y = 5x + 4x2
3y = 5x + 4x2

Add '-3y' to each side of the equation.
3y + -3y = 5x + 4x2 + -3y

Combine like terms: 3y + -3y = 0
0 = 5x + 4x2 + -3y

Simplifying
0 = 5x + 4x2 + -3y

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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