x(n)+2x(n-1)=3y(n)+6y(n-2)

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Solution for x(n)+2x(n-1)=3y(n)+6y(n-2) equation: 


Simplifying
x(n) + 2x(n + -1) = 3y(n) + 6y(n + -2)

Multiply x * n
nx + 2x(n + -1) = 3y(n) + 6y(n + -2)

Reorder the terms:
nx + 2x(-1 + n) = 3y(n) + 6y(n + -2)
nx + (-1 * 2x + n * 2x) = 3y(n) + 6y(n + -2)

Reorder the terms:
nx + (2nx + -2x) = 3y(n) + 6y(n + -2)
nx + (2nx + -2x) = 3y(n) + 6y(n + -2)

Combine like terms: nx + 2nx = 3nx
3nx + -2x = 3y(n) + 6y(n + -2)

Multiply y * n
3nx + -2x = 3ny + 6y(n + -2)

Reorder the terms:
3nx + -2x = 3ny + 6y(-2 + n)
3nx + -2x = 3ny + (-2 * 6y + n * 6y)

Reorder the terms:
3nx + -2x = 3ny + (6ny + -12y)
3nx + -2x = 3ny + (6ny + -12y)

Combine like terms: 3ny + 6ny = 9ny
3nx + -2x = 9ny + -12y

Solving
3nx + -2x = 9ny + -12y

Solving for variable 'n'.

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

Add '-9ny' to each side of the equation.
3nx + -9ny + -2x = 9ny + -9ny + -12y

Combine like terms: 9ny + -9ny = 0
3nx + -9ny + -2x = 0 + -12y
3nx + -9ny + -2x = -12y

Add '2x' to each side of the equation.
3nx + -9ny + -2x + 2x = 2x + -12y

Combine like terms: -2x + 2x = 0
3nx + -9ny + 0 = 2x + -12y
3nx + -9ny = 2x + -12y

Reorder the terms:
3nx + -9ny + -2x + 12y = 2x + -2x + -12y + 12y

Combine like terms: 2x + -2x = 0
3nx + -9ny + -2x + 12y = 0 + -12y + 12y
3nx + -9ny + -2x + 12y = -12y + 12y

Combine like terms: -12y + 12y = 0
3nx + -9ny + -2x + 12y = 0

The solution to this equation could not be determined.

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