y[n]-y[n-1]=x[n]-(2x[n-1])+(x[n-2])

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Solution for y[n]-y[n-1]=x[n]-(2x[n-1])+(x[n-2]) equation: 


Simplifying
y[n] + -1y[n + -1] = x[n] + -1(2x[n + -1]) + (x[n + -2])

Multiply y * n
ny + -1y[n + -1] = x[n] + -1(2x[n + -1]) + (x[n + -2])

Reorder the terms:
ny + -1y[-1 + n] = x[n] + -1(2x[n + -1]) + (x[n + -2])
ny + [-1 * -1y + n * -1y] = x[n] + -1(2x[n + -1]) + (x[n + -2])

Reorder the terms:
ny + [-1ny + 1y] = x[n] + -1(2x[n + -1]) + (x[n + -2])
ny + [-1ny + 1y] = x[n] + -1(2x[n + -1]) + (x[n + -2])

Combine like terms: ny + -1ny = 0
0 + 1y = x[n] + -1(2x[n + -1]) + (x[n + -2])
1y = x[n] + -1(2x[n + -1]) + (x[n + -2])

Multiply x * n
1y = nx + -1(2x[n + -1]) + (x[n + -2])

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

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

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

Reorder the terms:
1y = nx + -2nx + 2x + ([nx + -2x])
1y = nx + -2nx + 2x + ([nx + -2x])
1y = nx + -2nx + 2x + (nx + -2x)

Remove parenthesis around (nx + -2x)
1y = nx + -2nx + 2x + nx + -2x

Reorder the terms:
1y = nx + -2nx + nx + 2x + -2x

Combine like terms: nx + -2nx = -1nx
1y = -1nx + nx + 2x + -2x

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

Combine like terms: 2x + -2x = 0
1y = 0

Solving
1y = 0

Solving for variable 'y'.

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

Divide each side by '1'.
y = 0

Simplifying
y = 0

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