y(n)=0.5y(n-1)-0.06y(n-2)+x(n)-0.5x(n-2)

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Solution for y(n)=0.5y(n-1)-0.06y(n-2)+x(n)-0.5x(n-2) equation: 


Simplifying
y(n) = 0.5y(n + -1) + -0.06y(n + -2) + x(n) + -0.5x(n + -2)

Multiply y * n
ny = 0.5y(n + -1) + -0.06y(n + -2) + x(n) + -0.5x(n + -2)

Reorder the terms:
ny = 0.5y(-1 + n) + -0.06y(n + -2) + x(n) + -0.5x(n + -2)
ny = (-1 * 0.5y + n * 0.5y) + -0.06y(n + -2) + x(n) + -0.5x(n + -2)

Reorder the terms:
ny = (0.5ny + -0.5y) + -0.06y(n + -2) + x(n) + -0.5x(n + -2)
ny = (0.5ny + -0.5y) + -0.06y(n + -2) + x(n) + -0.5x(n + -2)

Reorder the terms:
ny = 0.5ny + -0.5y + -0.06y(-2 + n) + x(n) + -0.5x(n + -2)
ny = 0.5ny + -0.5y + (-2 * -0.06y + n * -0.06y) + x(n) + -0.5x(n + -2)

Reorder the terms:
ny = 0.5ny + -0.5y + (-0.06ny + 0.12y) + x(n) + -0.5x(n + -2)
ny = 0.5ny + -0.5y + (-0.06ny + 0.12y) + x(n) + -0.5x(n + -2)

Multiply x * n
ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + -0.5x(n + -2)

Reorder the terms:
ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + -0.5x(-2 + n)
ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + (-2 * -0.5x + n * -0.5x)

Reorder the terms:
ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + (-0.5nx + 1x)
ny = 0.5ny + -0.5y + -0.06ny + 0.12y + nx + (-0.5nx + 1x)

Reorder the terms:
ny = nx + -0.5nx + 0.5ny + -0.06ny + 1x + -0.5y + 0.12y

Combine like terms: nx + -0.5nx = 0.5nx
ny = 0.5nx + 0.5ny + -0.06ny + 1x + -0.5y + 0.12y

Combine like terms: 0.5ny + -0.06ny = 0.44ny
ny = 0.5nx + 0.44ny + 1x + -0.5y + 0.12y

Combine like terms: -0.5y + 0.12y = -0.38y
ny = 0.5nx + 0.44ny + 1x + -0.38y

Solving
ny = 0.5nx + 0.44ny + 1x + -0.38y

Solving for variable 'n'.

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

Add '-0.5nx' to each side of the equation.
-0.5nx + ny = 0.5nx + 0.44ny + 1x + -0.5nx + -0.38y

Reorder the terms:
-0.5nx + ny = 0.5nx + -0.5nx + 0.44ny + 1x + -0.38y

Combine like terms: 0.5nx + -0.5nx = 0.0
-0.5nx + ny = 0.0 + 0.44ny + 1x + -0.38y
-0.5nx + ny = 0.44ny + 1x + -0.38y

Add '-0.44ny' to each side of the equation.
-0.5nx + ny + -0.44ny = 0.44ny + 1x + -0.44ny + -0.38y

Combine like terms: ny + -0.44ny = 0.56ny
-0.5nx + 0.56ny = 0.44ny + 1x + -0.44ny + -0.38y

Reorder the terms:
-0.5nx + 0.56ny = 0.44ny + -0.44ny + 1x + -0.38y

Combine like terms: 0.44ny + -0.44ny = 0.00
-0.5nx + 0.56ny = 0.00 + 1x + -0.38y
-0.5nx + 0.56ny = 1x + -0.38y

Reorder the terms:
-0.5nx + 0.56ny + -1x + 0.38y = 1x + -1x + -0.38y + 0.38y

Combine like terms: 1x + -1x = 0
-0.5nx + 0.56ny + -1x + 0.38y = 0 + -0.38y + 0.38y
-0.5nx + 0.56ny + -1x + 0.38y = -0.38y + 0.38y

Combine like terms: -0.38y + 0.38y = 0.00
-0.5nx + 0.56ny + -1x + 0.38y = 0.00

The solution to this equation could not be determined.

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