y(n)-0.2y(n-1)=x(n)

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Solution for y(n)-0.2y(n-1)=x(n) equation: 


Simplifying
y(n) + -0.2y(n + -1) = x(n)

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

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

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

Combine like terms: ny + -0.2ny = 0.8ny
0.8ny + 0.2y = x(n)

Multiply x * n
0.8ny + 0.2y = nx

Solving
0.8ny + 0.2y = 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 + 0.2y = nx + -1nx

Reorder the terms:
-1nx + 0.8ny + 0.2y = nx + -1nx

Combine like terms: nx + -1nx = 0
-1nx + 0.8ny + 0.2y = 0

Add '-0.2y' to each side of the equation.
-1nx + 0.8ny + 0.2y + -0.2y = 0 + -0.2y

Combine like terms: 0.2y + -0.2y = 0.0
-1nx + 0.8ny + 0.0 = 0 + -0.2y
-1nx + 0.8ny = 0 + -0.2y
Remove the zero:
-1nx + 0.8ny = -0.2y

Combine like terms: -0.2y + 0.2y = 0.0
-1nx + 0.8ny + 0.2y = 0.0

The solution to this equation could not be determined.

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