(2x+6y)dx+(6x+3y)dy=0

Simple and best practice solution for (2x+6y)dx+(6x+3y)dy=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (2x+6y)dx+(6x+3y)dy=0 equation: 


Simplifying
(2x + 6y) * dx + (6x + 3y) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + 6y) + (6x + 3y) * dy = 0
(2x * dx + 6y * dx) + (6x + 3y) * dy = 0

Reorder the terms:
(6dxy + 2dx2) + (6x + 3y) * dy = 0
(6dxy + 2dx2) + (6x + 3y) * dy = 0

Reorder the terms for easier multiplication:
6dxy + 2dx2 + dy(6x + 3y) = 0
6dxy + 2dx2 + (6x * dy + 3y * dy) = 0
6dxy + 2dx2 + (6dxy + 3dy2) = 0

Reorder the terms:
6dxy + 6dxy + 2dx2 + 3dy2 = 0

Combine like terms: 6dxy + 6dxy = 12dxy
12dxy + 2dx2 + 3dy2 = 0

Solving
12dxy + 2dx2 + 3dy2 = 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(12xy + 2x2 + 3y2) = 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 '(12xy + 2x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
12xy + 2x2 + 3y2 = 0

Solving
12xy + 2x2 + 3y2 = 0

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

Add '-12xy' to each side of the equation.
12xy + 2x2 + -12xy + 3y2 = 0 + -12xy

Reorder the terms:
12xy + -12xy + 2x2 + 3y2 = 0 + -12xy

Combine like terms: 12xy + -12xy = 0
0 + 2x2 + 3y2 = 0 + -12xy
2x2 + 3y2 = 0 + -12xy
Remove the zero:
2x2 + 3y2 = -12xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 3y2 = -12xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 3y2 = -12xy + -2x2
3y2 = -12xy + -2x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -12xy + -2x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -12xy + -2x2 + -3y2

Simplifying
0 = -12xy + -2x2 + -3y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

See similar equations:

| -8+4x=-8 | | 3/2+2/5= | | 25n=225 | | 6+5(x-7)=5-9(x-4) | | -2x^2=19x+33 | | 3x+1(x-4)=4x+7 | | 3+-4x+x*x=0 | | -3x+-15=26x | | N+3+3n=15 | | 5x+3(x+2)=22 | | x(18-3x)=0 | | -5(n+4)+24=-2n-2 | | 5(x-8)+12=2(x-5) | | 75=5r | | 6y+3+6y+3+6y+3+6y+3=90 | | 3x+-5=7x+-11 | | 0=48-8x-x^4 | | 2800000=2000000 | | 4(5x+8)=20x-2 | | y^2-6y=47 | | 10k+1-6k= | | x^4=800000 | | -2k-7=-3 | | 2m^2-13m+11=0 | | 3x-5(x-5)=-8+4x+3 | | SecosX=0 | | 6p+3= | | SecosX=9 | | 40-8=5 | | 3.1x+51.3=23.9-10.6x | | X+6=3[3-x] | | 3ln(5x+4)=18 |

Equations solver categories