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

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

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

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

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

Reorder the terms:
ny + -0.1 + 0.1n + 0.2(-2 + n) = x(n)
ny + -0.1 + 0.1n + (-2 * 0.2 + n * 0.2) = x(n)
ny + -0.1 + 0.1n + (-0.4 + 0.2n) = x(n)

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

Combine like terms: -0.1 + -0.4 = -0.5
-0.5 + 0.1n + 0.2n + ny = x(n)

Combine like terms: 0.1n + 0.2n = 0.3n
-0.5 + 0.3n + ny = x(n)

Multiply x * n
-0.5 + 0.3n + ny = nx

Solving
-0.5 + 0.3n + ny = 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.
-0.5 + 0.3n + -1nx + ny = nx + -1nx

Combine like terms: nx + -1nx = 0
-0.5 + 0.3n + -1nx + ny = 0

Add '0.5' to each side of the equation.
-0.5 + 0.3n + -1nx + 0.5 + ny = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3n + -1nx + ny = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3n + -1nx + ny = 0 + 0.5
0.3n + -1nx + ny = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.3n + -1nx + ny = 0.5

Reorder the terms:
-0.5 + 0.3n + -1nx + ny = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + 0.3n + -1nx + ny = 0.0

The solution to this equation could not be determined.