y(n)+4y(n-1)+3y(n-2)=x(n-1)

Solution for y(n)+4y(n-1)+3y(n-2)=x(n-1) equation:

Simplifying
y(n) + 4y(n + -1) + 3y(n + -2) = x(n + -1)

Multiply y * n
ny + 4y(n + -1) + 3y(n + -2) = x(n + -1)

Reorder the terms:
ny + 4y(-1 + n) + 3y(n + -2) = x(n + -1)
ny + (-1 * 4y + n * 4y) + 3y(n + -2) = x(n + -1)

Reorder the terms:
ny + (4ny + -4y) + 3y(n + -2) = x(n + -1)
ny + (4ny + -4y) + 3y(n + -2) = x(n + -1)

Reorder the terms:
ny + 4ny + -4y + 3y(-2 + n) = x(n + -1)
ny + 4ny + -4y + (-2 * 3y + n * 3y) = x(n + -1)

Reorder the terms:
ny + 4ny + -4y + (3ny + -6y) = x(n + -1)
ny + 4ny + -4y + (3ny + -6y) = x(n + -1)

Reorder the terms:
ny + 4ny + 3ny + -4y + -6y = x(n + -1)

Combine like terms: ny + 4ny = 5ny
5ny + 3ny + -4y + -6y = x(n + -1)

Combine like terms: 5ny + 3ny = 8ny
8ny + -4y + -6y = x(n + -1)

Combine like terms: -4y + -6y = -10y
8ny + -10y = x(n + -1)

Reorder the terms:
8ny + -10y = x(-1 + n)
8ny + -10y = (-1 * x + n * x)

Reorder the terms:
8ny + -10y = (nx + -1x)
8ny + -10y = (nx + -1x)

Solving
8ny + -10y = nx + -1x

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.
8ny + -1nx + -10y = nx + -1nx + -1x

Reorder the terms:
-1nx + 8ny + -10y = nx + -1nx + -1x

Combine like terms: nx + -1nx = 0
-1nx + 8ny + -10y = 0 + -1x
-1nx + 8ny + -10y = -1x

Add '10y' to each side of the equation.
-1nx + 8ny + -10y + 10y = -1x + 10y

Combine like terms: -10y + 10y = 0
-1nx + 8ny + 0 = -1x + 10y
-1nx + 8ny = -1x + 10y

Reorder the terms:
-1nx + 8ny + x + -10y = -1x + x + 10y + -10y

Combine like terms: -1x + x = 0
-1nx + 8ny + x + -10y = 0 + 10y + -10y
-1nx + 8ny + x + -10y = 10y + -10y

Combine like terms: 10y + -10y = 0
-1nx + 8ny + x + -10y = 0

The solution to this equation could not be determined.