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

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

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

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

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

Reorder the terms:
4n = 2 + -3 + 2n + 3n

Combine like terms: 2 + -3 = -1
4n = -1 + 2n + 3n

Combine like terms: 2n + 3n = 5n
4n = -1 + 5n

Solving
4n = -1 + 5n

Solving for variable 'n'.

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

Add '-5n' to each side of the equation.
4n + -5n = -1 + 5n + -5n

Combine like terms: 4n + -5n = -1n
-1n = -1 + 5n + -5n

Combine like terms: 5n + -5n = 0
-1n = -1 + 0
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1