y(n)+y(n-1)+.5*y(n-2)+.25*y(n-3)=x(n)

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Solution for y(n)+y(n-1)+.5*y(n-2)+.25*y(n-3)=x(n) equation: 


Simplifying
y(n) + y(n + -1) + 0.5y(n + -2) + 0.25y(n + -3) = x(n)

Multiply y * n
ny + y(n + -1) + 0.5y(n + -2) + 0.25y(n + -3) = x(n)

Reorder the terms:
ny + y(-1 + n) + 0.5y(n + -2) + 0.25y(n + -3) = x(n)
ny + (-1 * y + n * y) + 0.5y(n + -2) + 0.25y(n + -3) = x(n)

Reorder the terms:
ny + (ny + -1y) + 0.5y(n + -2) + 0.25y(n + -3) = x(n)
ny + (ny + -1y) + 0.5y(n + -2) + 0.25y(n + -3) = x(n)

Reorder the terms:
ny + ny + -1y + 0.5y(-2 + n) + 0.25y(n + -3) = x(n)
ny + ny + -1y + (-2 * 0.5y + n * 0.5y) + 0.25y(n + -3) = x(n)

Reorder the terms:
ny + ny + -1y + (0.5ny + -1y) + 0.25y(n + -3) = x(n)
ny + ny + -1y + (0.5ny + -1y) + 0.25y(n + -3) = x(n)

Reorder the terms:
ny + ny + -1y + 0.5ny + -1y + 0.25y(-3 + n) = x(n)
ny + ny + -1y + 0.5ny + -1y + (-3 * 0.25y + n * 0.25y) = x(n)

Reorder the terms:
ny + ny + -1y + 0.5ny + -1y + (0.25ny + -0.75y) = x(n)
ny + ny + -1y + 0.5ny + -1y + (0.25ny + -0.75y) = x(n)

Reorder the terms:
ny + ny + 0.5ny + 0.25ny + -1y + -1y + -0.75y = x(n)

Combine like terms: ny + ny = 2ny
2ny + 0.5ny + 0.25ny + -1y + -1y + -0.75y = x(n)

Combine like terms: 2ny + 0.5ny = 2.5ny
2.5ny + 0.25ny + -1y + -1y + -0.75y = x(n)

Combine like terms: 2.5ny + 0.25ny = 2.75ny
2.75ny + -1y + -1y + -0.75y = x(n)

Combine like terms: -1y + -1y = -2y
2.75ny + -2y + -0.75y = x(n)

Combine like terms: -2y + -0.75y = -2.75y
2.75ny + -2.75y = x(n)

Multiply x * n
2.75ny + -2.75y = nx

Solving
2.75ny + -2.75y = nx

Solving for variable 'n'.

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

Add '-1nx' to each side of the equation.
2.75ny + -1nx + -2.75y = nx + -1nx

Reorder the terms:
-1nx + 2.75ny + -2.75y = nx + -1nx

Combine like terms: nx + -1nx = 0
-1nx + 2.75ny + -2.75y = 0

Add '2.75y' to each side of the equation.
-1nx + 2.75ny + -2.75y + 2.75y = 0 + 2.75y

Combine like terms: -2.75y + 2.75y = 0.00
-1nx + 2.75ny + 0.00 = 0 + 2.75y
-1nx + 2.75ny = 0 + 2.75y
Remove the zero:
-1nx + 2.75ny = 2.75y

Combine like terms: 2.75y + -2.75y = 0.00
-1nx + 2.75ny + -2.75y = 0.00

The solution to this equation could not be determined.

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