6[n-1]=2[n+1]

Solution for 6[n-1]=2[n+1] equation:

Simplifying
6[n + -1] = 2[n + 1]

Reorder the terms:
6[-1 + n] = 2[n + 1]
[-1 * 6 + n * 6] = 2[n + 1]
[-6 + 6n] = 2[n + 1]

Reorder the terms:
-6 + 6n = 2[1 + n]
-6 + 6n = [1 * 2 + n * 2]
-6 + 6n = [2 + 2n]

Solving
-6 + 6n = 2 + 2n

Solving for variable 'n'.

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

Add '-2n' to each side of the equation.
-6 + 6n + -2n = 2 + 2n + -2n

Combine like terms: 6n + -2n = 4n
-6 + 4n = 2 + 2n + -2n

Combine like terms: 2n + -2n = 0
-6 + 4n = 2 + 0
-6 + 4n = 2

Add '6' to each side of the equation.
-6 + 6 + 4n = 2 + 6

Combine like terms: -6 + 6 = 0
0 + 4n = 2 + 6
4n = 2 + 6

Combine like terms: 2 + 6 = 8
4n = 8

Divide each side by '4'.
n = 2

Simplifying
n = 2