y[n]=x[n]+2x[n-2]+0.7y[n-1]

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Solution for y[n]=x[n]+2x[n-2]+0.7y[n-1] equation: 


Simplifying
y[n] = x[n] + 2x[n + -2] + 0.7y[n + -1]

Multiply y * n
ny = x[n] + 2x[n + -2] + 0.7y[n + -1]

Multiply x * n
ny = nx + 2x[n + -2] + 0.7y[n + -1]

Reorder the terms:
ny = nx + 2x[-2 + n] + 0.7y[n + -1]
ny = nx + [-2 * 2x + n * 2x] + 0.7y[n + -1]

Reorder the terms:
ny = nx + [2nx + -4x] + 0.7y[n + -1]
ny = nx + [2nx + -4x] + 0.7y[n + -1]

Reorder the terms:
ny = nx + 2nx + -4x + 0.7y[-1 + n]
ny = nx + 2nx + -4x + [-1 * 0.7y + n * 0.7y]

Reorder the terms:
ny = nx + 2nx + -4x + [0.7ny + -0.7y]
ny = nx + 2nx + -4x + [0.7ny + -0.7y]

Reorder the terms:
ny = nx + 2nx + 0.7ny + -4x + -0.7y

Combine like terms: nx + 2nx = 3nx
ny = 3nx + 0.7ny + -4x + -0.7y

Solving
ny = 3nx + 0.7ny + -4x + -0.7y

Solving for variable 'n'.

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

Add '-3nx' to each side of the equation.
-3nx + ny = 3nx + 0.7ny + -4x + -3nx + -0.7y

Reorder the terms:
-3nx + ny = 3nx + -3nx + 0.7ny + -4x + -0.7y

Combine like terms: 3nx + -3nx = 0
-3nx + ny = 0 + 0.7ny + -4x + -0.7y
-3nx + ny = 0.7ny + -4x + -0.7y

Add '-0.7ny' to each side of the equation.
-3nx + ny + -0.7ny = 0.7ny + -4x + -0.7ny + -0.7y

Combine like terms: ny + -0.7ny = 0.3ny
-3nx + 0.3ny = 0.7ny + -4x + -0.7ny + -0.7y

Reorder the terms:
-3nx + 0.3ny = 0.7ny + -0.7ny + -4x + -0.7y

Combine like terms: 0.7ny + -0.7ny = 0.0
-3nx + 0.3ny = 0.0 + -4x + -0.7y
-3nx + 0.3ny = -4x + -0.7y

Reorder the terms:
-3nx + 0.3ny + 4x + 0.7y = -4x + 4x + -0.7y + 0.7y

Combine like terms: -4x + 4x = 0
-3nx + 0.3ny + 4x + 0.7y = 0 + -0.7y + 0.7y
-3nx + 0.3ny + 4x + 0.7y = -0.7y + 0.7y

Combine like terms: -0.7y + 0.7y = 0.0
-3nx + 0.3ny + 4x + 0.7y = 0.0

The solution to this equation could not be determined.

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