0.2y(n)-0.1y(n-1)+0.7y(n-3)=x(n)

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Solution for 0.2y(n)-0.1y(n-1)+0.7y(n-3)=x(n) equation: 


Simplifying
0.2y(n) + -0.1y(n + -1) + 0.7y(n + -3) = x(n)

Multiply y * n
0.2ny + -0.1y(n + -1) + 0.7y(n + -3) = x(n)

Reorder the terms:
0.2ny + -0.1y(-1 + n) + 0.7y(n + -3) = x(n)
0.2ny + (-1 * -0.1y + n * -0.1y) + 0.7y(n + -3) = x(n)

Reorder the terms:
0.2ny + (-0.1ny + 0.1y) + 0.7y(n + -3) = x(n)
0.2ny + (-0.1ny + 0.1y) + 0.7y(n + -3) = x(n)

Reorder the terms:
0.2ny + -0.1ny + 0.1y + 0.7y(-3 + n) = x(n)
0.2ny + -0.1ny + 0.1y + (-3 * 0.7y + n * 0.7y) = x(n)

Reorder the terms:
0.2ny + -0.1ny + 0.1y + (0.7ny + -2.1y) = x(n)
0.2ny + -0.1ny + 0.1y + (0.7ny + -2.1y) = x(n)

Reorder the terms:
0.2ny + -0.1ny + 0.7ny + 0.1y + -2.1y = x(n)

Combine like terms: 0.2ny + -0.1ny = 0.1ny
0.1ny + 0.7ny + 0.1y + -2.1y = x(n)

Combine like terms: 0.1ny + 0.7ny = 0.8ny
0.8ny + 0.1y + -2.1y = x(n)

Combine like terms: 0.1y + -2.1y = -2y
0.8ny + -2y = x(n)

Multiply x * n
0.8ny + -2y = nx

Solving
0.8ny + -2y = nx

Solving for variable 'n'.

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

Add '-1nx' to each side of the equation.
0.8ny + -1nx + -2y = nx + -1nx

Reorder the terms:
-1nx + 0.8ny + -2y = nx + -1nx

Combine like terms: nx + -1nx = 0
-1nx + 0.8ny + -2y = 0

Add '2y' to each side of the equation.
-1nx + 0.8ny + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-1nx + 0.8ny + 0 = 0 + 2y
-1nx + 0.8ny = 0 + 2y
Remove the zero:
-1nx + 0.8ny = 2y

Combine like terms: 2y + -2y = 0
-1nx + 0.8ny + -2y = 0

The solution to this equation could not be determined.

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