y(n)+0.1y(n-1)+0.2y(n-2)=x(n)

Solution for y(n)+0.1y(n-1)+0.2y(n-2)=x(n) equation:

Simplifying
y(n) + 0.1y(n + -1) + 0.2y(n + -2) = x(n)

Multiply y * n
ny + 0.1y(n + -1) + 0.2y(n + -2) = x(n)

Reorder the terms:
ny + 0.1y(-1 + n) + 0.2y(n + -2) = x(n)
ny + (-1 * 0.1y + n * 0.1y) + 0.2y(n + -2) = x(n)

Reorder the terms:
ny + (0.1ny + -0.1y) + 0.2y(n + -2) = x(n)
ny + (0.1ny + -0.1y) + 0.2y(n + -2) = x(n)

Reorder the terms:
ny + 0.1ny + -0.1y + 0.2y(-2 + n) = x(n)
ny + 0.1ny + -0.1y + (-2 * 0.2y + n * 0.2y) = x(n)

Reorder the terms:
ny + 0.1ny + -0.1y + (0.2ny + -0.4y) = x(n)
ny + 0.1ny + -0.1y + (0.2ny + -0.4y) = x(n)

Reorder the terms:
ny + 0.1ny + 0.2ny + -0.1y + -0.4y = x(n)

Combine like terms: ny + 0.1ny = 1.1ny
1.1ny + 0.2ny + -0.1y + -0.4y = x(n)

Combine like terms: 1.1ny + 0.2ny = 1.3ny
1.3ny + -0.1y + -0.4y = x(n)

Combine like terms: -0.1y + -0.4y = -0.5y
1.3ny + -0.5y = x(n)

Multiply x * n
1.3ny + -0.5y = nx

Solving
1.3ny + -0.5y = 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.
1.3ny + -1nx + -0.5y = nx + -1nx

Reorder the terms:
-1nx + 1.3ny + -0.5y = nx + -1nx

Combine like terms: nx + -1nx = 0
-1nx + 1.3ny + -0.5y = 0

Add '0.5y' to each side of the equation.
-1nx + 1.3ny + -0.5y + 0.5y = 0 + 0.5y

Combine like terms: -0.5y + 0.5y = 0.0
-1nx + 1.3ny + 0.0 = 0 + 0.5y
-1nx + 1.3ny = 0 + 0.5y
Remove the zero:
-1nx + 1.3ny = 0.5y

Combine like terms: 0.5y + -0.5y = 0.0
-1nx + 1.3ny + -0.5y = 0.0

The solution to this equation could not be determined.