y[n]-0.4y[n-1]=2r[n]

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Solution for y[n]-0.4y[n-1]=2r[n] equation: 


Simplifying
y[n] + -0.4y[n + -1] = 2r[n]

Multiply y * n
ny + -0.4y[n + -1] = 2r[n]

Reorder the terms:
ny + -0.4y[-1 + n] = 2r[n]
ny + [-1 * -0.4y + n * -0.4y] = 2r[n]

Reorder the terms:
ny + [-0.4ny + 0.4y] = 2r[n]
ny + [-0.4ny + 0.4y] = 2r[n]

Combine like terms: ny + -0.4ny = 0.6ny
0.6ny + 0.4y = 2r[n]

Multiply r * n
0.6ny + 0.4y = 2nr

Solving
0.6ny + 0.4y = 2nr

Solving for variable 'n'.

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

Add '-2nr' to each side of the equation.
0.6ny + -2nr + 0.4y = 2nr + -2nr

Reorder the terms:
-2nr + 0.6ny + 0.4y = 2nr + -2nr

Combine like terms: 2nr + -2nr = 0
-2nr + 0.6ny + 0.4y = 0

Add '-0.4y' to each side of the equation.
-2nr + 0.6ny + 0.4y + -0.4y = 0 + -0.4y

Combine like terms: 0.4y + -0.4y = 0.0
-2nr + 0.6ny + 0.0 = 0 + -0.4y
-2nr + 0.6ny = 0 + -0.4y
Remove the zero:
-2nr + 0.6ny = -0.4y

Combine like terms: -0.4y + 0.4y = 0.0
-2nr + 0.6ny + 0.4y = 0.0

The solution to this equation could not be determined.

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