y[n]+0.2[n-1]=x[n]x[n-1]

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Solution for y[n]+0.2[n-1]=x[n]x[n-1] equation:


Simplifying
y[n] + 0.2[n + -1] = x[n] * x[n + -1]

Multiply y * n
ny + 0.2[n + -1] = x[n] * x[n + -1]

Reorder the terms:
ny + 0.2[-1 + n] = x[n] * x[n + -1]
ny + [-1 * 0.2 + n * 0.2] = x[n] * x[n + -1]
ny + [-0.2 + 0.2n] = x[n] * x[n + -1]

Reorder the terms:
-0.2 + 0.2n + ny = x[n] * x[n + -1]

Reorder the terms:
-0.2 + 0.2n + ny = x * n * x[-1 + n]

Multiply x * n
-0.2 + 0.2n + ny = nx * x[-1 + n]

Multiply nx * x
-0.2 + 0.2n + ny = nx2[-1 + n]
-0.2 + 0.2n + ny = [-1 * nx2 + n * nx2]
-0.2 + 0.2n + ny = [-1nx2 + n2x2]

Solving
-0.2 + 0.2n + ny = -1nx2 + n2x2

Solving for variable 'n'.

Reorder the terms:
-0.2 + 0.2n + nx2 + ny + -1n2x2 = -1nx2 + n2x2 + nx2 + -1n2x2

Reorder the terms:
-0.2 + 0.2n + nx2 + ny + -1n2x2 = -1nx2 + nx2 + n2x2 + -1n2x2

Combine like terms: -1nx2 + nx2 = 0
-0.2 + 0.2n + nx2 + ny + -1n2x2 = 0 + n2x2 + -1n2x2
-0.2 + 0.2n + nx2 + ny + -1n2x2 = n2x2 + -1n2x2

Combine like terms: n2x2 + -1n2x2 = 0
-0.2 + 0.2n + nx2 + ny + -1n2x2 = 0

The solution to this equation could not be determined.

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