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

Simple and best practice solution for (2x+6y)dx+(6x+2y)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+2y)dy=0 equation: 


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

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

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

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

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

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

Solving
12dxy + 2dx2 + 2dy2 = 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), '2d'.
2d(6xy + x2 + y2) = 0

Ignore the factor 2.

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 '(6xy + x2 + y2)' equal to zero and attempt to solve:

Simplifying
6xy + x2 + y2 = 0

Solving
6xy + x2 + y2 = 0

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

Add '-6xy' to each side of the equation.
6xy + x2 + -6xy + y2 = 0 + -6xy

Reorder the terms:
6xy + -6xy + x2 + y2 = 0 + -6xy

Combine like terms: 6xy + -6xy = 0
0 + x2 + y2 = 0 + -6xy
x2 + y2 = 0 + -6xy
Remove the zero:
x2 + y2 = -6xy

Add '-1x2' to each side of the equation.
x2 + -1x2 + y2 = -6xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + y2 = -6xy + -1x2
y2 = -6xy + -1x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -6xy + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -6xy + -1x2 + -1y2

Simplifying
0 = -6xy + -1x2 + -1y2

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:

| h(x)=-0.8x^2+2.4x+6 | | x/x-6=3/x-8 | | -7(n+7)=-29-3n | | 6x+9=9x+18 | | 3(6x-2)=11x+8 | | 3x-16=25 | | x^4-2x^3+2x^2+6x-15=0 | | 11/8y-13=-2 | | 4p+9=11 | | -4(-2a-4)=6a+4 | | 1/4×1/4 | | 27y^2-4x=0 | | (9x^2)/15x | | 7y+3=10y-12 | | 11/2≥3x-2 | | 13=2-y | | 4x^2-4x-5=8x+6 | | 284.7-14.6= | | 31+5=11 | | -3(4x+3)+4(6x+1)+4(6x+1)=43 | | 16(2.8125+0.9375a)=45+15a | | 13=2+y | | -m-8(4m-2)=-23+6m | | 28x-36=35x+13 | | 1.1=13.9-8w | | 16b=45+15a | | 7/x-1/6=x | | 3(x-4)-2(5x-4)-7x= | | 3(11/2)+2= | | (5x+3)(2x-4u-2)= | | -3(5y-9)-3(4y-4)-14y= | | -4^3/-4^2-4 |

Equations solver categories