2y(n)-y(n-2)=3y(n-1)+0.3x(n)-4x(n-3)

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Solution for 2y(n)-y(n-2)=3y(n-1)+0.3x(n)-4x(n-3) equation: 


Simplifying
2y(n) + -1y(n + -2) = 3y(n + -1) + 0.3x(n) + -4x(n + -3)

Multiply y * n
2ny + -1y(n + -2) = 3y(n + -1) + 0.3x(n) + -4x(n + -3)

Reorder the terms:
2ny + -1y(-2 + n) = 3y(n + -1) + 0.3x(n) + -4x(n + -3)
2ny + (-2 * -1y + n * -1y) = 3y(n + -1) + 0.3x(n) + -4x(n + -3)

Reorder the terms:
2ny + (-1ny + 2y) = 3y(n + -1) + 0.3x(n) + -4x(n + -3)
2ny + (-1ny + 2y) = 3y(n + -1) + 0.3x(n) + -4x(n + -3)

Combine like terms: 2ny + -1ny = 1ny
1ny + 2y = 3y(n + -1) + 0.3x(n) + -4x(n + -3)

Reorder the terms:
1ny + 2y = 3y(-1 + n) + 0.3x(n) + -4x(n + -3)
1ny + 2y = (-1 * 3y + n * 3y) + 0.3x(n) + -4x(n + -3)

Reorder the terms:
1ny + 2y = (3ny + -3y) + 0.3x(n) + -4x(n + -3)
1ny + 2y = (3ny + -3y) + 0.3x(n) + -4x(n + -3)

Multiply x * n
1ny + 2y = 3ny + -3y + 0.3nx + -4x(n + -3)

Reorder the terms:
1ny + 2y = 3ny + -3y + 0.3nx + -4x(-3 + n)
1ny + 2y = 3ny + -3y + 0.3nx + (-3 * -4x + n * -4x)

Reorder the terms:
1ny + 2y = 3ny + -3y + 0.3nx + (-4nx + 12x)
1ny + 2y = 3ny + -3y + 0.3nx + (-4nx + 12x)

Reorder the terms:
1ny + 2y = 0.3nx + -4nx + 3ny + 12x + -3y

Combine like terms: 0.3nx + -4nx = -3.7nx
1ny + 2y = -3.7nx + 3ny + 12x + -3y

Solving
1ny + 2y = -3.7nx + 3ny + 12x + -3y

Solving for variable 'n'.

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

Add '3.7nx' to each side of the equation.
1ny + 3.7nx + 2y = -3.7nx + 3ny + 12x + 3.7nx + -3y

Reorder the terms:
3.7nx + 1ny + 2y = -3.7nx + 3ny + 12x + 3.7nx + -3y

Reorder the terms:
3.7nx + 1ny + 2y = -3.7nx + 3.7nx + 3ny + 12x + -3y

Combine like terms: -3.7nx + 3.7nx = 0.0
3.7nx + 1ny + 2y = 0.0 + 3ny + 12x + -3y
3.7nx + 1ny + 2y = 3ny + 12x + -3y

Add '-3ny' to each side of the equation.
3.7nx + 1ny + -3ny + 2y = 3ny + 12x + -3ny + -3y

Combine like terms: 1ny + -3ny = -2ny
3.7nx + -2ny + 2y = 3ny + 12x + -3ny + -3y

Reorder the terms:
3.7nx + -2ny + 2y = 3ny + -3ny + 12x + -3y

Combine like terms: 3ny + -3ny = 0
3.7nx + -2ny + 2y = 0 + 12x + -3y
3.7nx + -2ny + 2y = 12x + -3y

Add '-2y' to each side of the equation.
3.7nx + -2ny + 2y + -2y = 12x + -3y + -2y

Combine like terms: 2y + -2y = 0
3.7nx + -2ny + 0 = 12x + -3y + -2y
3.7nx + -2ny = 12x + -3y + -2y

Combine like terms: -3y + -2y = -5y
3.7nx + -2ny = 12x + -5y

Reorder the terms:
3.7nx + -2ny + -12x + 5y = 12x + -12x + -5y + 5y

Combine like terms: 12x + -12x = 0
3.7nx + -2ny + -12x + 5y = 0 + -5y + 5y
3.7nx + -2ny + -12x + 5y = -5y + 5y

Combine like terms: -5y + 5y = 0
3.7nx + -2ny + -12x + 5y = 0

The solution to this equation could not be determined.

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