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

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

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

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

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

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

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

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

Combine like terms: -1a + -2a = -3a
an = 3(-3a + 3a + an + an + -1an)

Combine like terms: -3a + 3a = 0
an = 3(0 + an + an + -1an)
an = 3(an + an + -1an)

Combine like terms: an + an = 2an
an = 3(2an + -1an)

Combine like terms: 2an + -1an = 1an
an = 3(1an)

Remove parenthesis around (1an)
an = 3 * 1an

Multiply 3 * 1
an = 3an

Solving
an = 3an

Solving for variable 'a'.

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

Add '-3an' to each side of the equation.
an + -3an = 3an + -3an

Combine like terms: an + -3an = -2an
-2an = 3an + -3an

Combine like terms: 3an + -3an = 0
-2an = 0

Divide each side by '-2'.
an = 0

Simplifying
an = 0

The solution to this equation could not be determined.