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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
ny = -1nx + 2x * x[-1 + n][-2 + n]

Multiply x * x
ny = -1nx + 2x2[-1 + n][-2 + n]

Multiply [-1 + n] * [-2 + n]
ny = -1nx + 2x2[-1[-2 + n] + n[-2 + n]]
ny = -1nx + 2x2[[-2 * -1 + n * -1] + n[-2 + n]]
ny = -1nx + 2x2[[2 + -1n] + n[-2 + n]]
ny = -1nx + 2x2[2 + -1n + [-2 * n + n * n]]
ny = -1nx + 2x2[2 + -1n + [-2n + n2]]

Combine like terms: -1n + -2n = -3n
ny = -1nx + 2x2[2 + -3n + n2]
ny = -1nx + [2 * 2x2 + -3n * 2x2 + n2 * 2x2]

Reorder the terms:
ny = -1nx + [-6nx2 + 2n2x2 + 4x2]
ny = -1nx + [-6nx2 + 2n2x2 + 4x2]

Solving
ny = -1nx + -6nx2 + 2n2x2 + 4x2

Solving for variable 'n'.

Reorder the terms:
nx + 6nx2 + ny + -2n2x2 + -4x2 = -1nx + -6nx2 + 2n2x2 + 4x2 + nx + 6nx2 + -2n2x2 + -4x2

Reorder the terms:
nx + 6nx2 + ny + -2n2x2 + -4x2 = -1nx + nx + -6nx2 + 6nx2 + 2n2x2 + -2n2x2 + 4x2 + -4x2

Combine like terms: -1nx + nx = 0
nx + 6nx2 + ny + -2n2x2 + -4x2 = 0 + -6nx2 + 6nx2 + 2n2x2 + -2n2x2 + 4x2 + -4x2
nx + 6nx2 + ny + -2n2x2 + -4x2 = -6nx2 + 6nx2 + 2n2x2 + -2n2x2 + 4x2 + -4x2

Combine like terms: -6nx2 + 6nx2 = 0
nx + 6nx2 + ny + -2n2x2 + -4x2 = 0 + 2n2x2 + -2n2x2 + 4x2 + -4x2
nx + 6nx2 + ny + -2n2x2 + -4x2 = 2n2x2 + -2n2x2 + 4x2 + -4x2

Combine like terms: 2n2x2 + -2n2x2 = 0
nx + 6nx2 + ny + -2n2x2 + -4x2 = 0 + 4x2 + -4x2
nx + 6nx2 + ny + -2n2x2 + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
nx + 6nx2 + ny + -2n2x2 + -4x2 = 0

The solution to this equation could not be determined.

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