a(n)=a(n-1)+3*a(n-3)+10*n+2

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Solution for a(n)=a(n-1)+3*a(n-3)+10*n+2 equation: 


Simplifying
a(n) = a(n + -1) + 3a(n + -3) + 10n + 2

Multiply a * n
an = a(n + -1) + 3a(n + -3) + 10n + 2

Reorder the terms:
an = a(-1 + n) + 3a(n + -3) + 10n + 2
an = (-1 * a + n * a) + 3a(n + -3) + 10n + 2
an = (-1a + an) + 3a(n + -3) + 10n + 2

Reorder the terms:
an = -1a + an + 3a(-3 + n) + 10n + 2
an = -1a + an + (-3 * 3a + n * 3a) + 10n + 2
an = -1a + an + (-9a + 3an) + 10n + 2

Reorder the terms:
an = 2 + -1a + -9a + an + 3an + 10n

Combine like terms: -1a + -9a = -10a
an = 2 + -10a + an + 3an + 10n

Combine like terms: an + 3an = 4an
an = 2 + -10a + 4an + 10n

Solving
an = 2 + -10a + 4an + 10n

Solving for variable 'a'.

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

Add '10a' to each side of the equation.
10a + an = 2 + -10a + 4an + 10a + 10n

Reorder the terms:
10a + an = 2 + -10a + 10a + 4an + 10n

Combine like terms: -10a + 10a = 0
10a + an = 2 + 0 + 4an + 10n
10a + an = 2 + 4an + 10n

Add '-4an' to each side of the equation.
10a + an + -4an = 2 + 4an + -4an + 10n

Combine like terms: an + -4an = -3an
10a + -3an = 2 + 4an + -4an + 10n

Combine like terms: 4an + -4an = 0
10a + -3an = 2 + 0 + 10n
10a + -3an = 2 + 10n

Reorder the terms:
-2 + 10a + -3an + -10n = 2 + 10n + -2 + -10n

Reorder the terms:
-2 + 10a + -3an + -10n = 2 + -2 + 10n + -10n

Combine like terms: 2 + -2 = 0
-2 + 10a + -3an + -10n = 0 + 10n + -10n
-2 + 10a + -3an + -10n = 10n + -10n

Combine like terms: 10n + -10n = 0
-2 + 10a + -3an + -10n = 0

The solution to this equation could not be determined.

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