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

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


Simplifying
y[n] = x2[n] + -1x[n + -1] * x[n + -2]

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

Multiply x2 * n
ny = nx2 + -1x[n + -1] * x[n + -2]

Reorder the terms:
ny = nx2 + -1x[-1 + n] * x[n + -2]

Reorder the terms:
ny = nx2 + -1x[-1 + n] * x[-2 + n]

Reorder the terms for easier multiplication:
ny = nx2 + -1x * x[-1 + n][-2 + n]

Multiply x * x
ny = nx2 + -1x2[-1 + n][-2 + n]

Multiply [-1 + n] * [-2 + n]
ny = nx2 + -1x2[-1[-2 + n] + n[-2 + n]]
ny = nx2 + -1x2[[-2 * -1 + n * -1] + n[-2 + n]]
ny = nx2 + -1x2[[2 + -1n] + n[-2 + n]]
ny = nx2 + -1x2[2 + -1n + [-2 * n + n * n]]
ny = nx2 + -1x2[2 + -1n + [-2n + n2]]

Combine like terms: -1n + -2n = -3n
ny = nx2 + -1x2[2 + -3n + n2]
ny = nx2 + [2 * -1x2 + -3n * -1x2 + n2 * -1x2]

Reorder the terms:
ny = nx2 + [3nx2 + -1n2x2 + -2x2]
ny = nx2 + [3nx2 + -1n2x2 + -2x2]

Combine like terms: nx2 + 3nx2 = 4nx2
ny = 4nx2 + -1n2x2 + -2x2

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

Solving for variable 'n'.

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

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

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

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

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

The solution to this equation could not be determined.

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