2(n-5)+1=(n-3)-(n-2)

Solution for 2(n-5)+1=(n-3)-(n-2) equation:

Simplifying
2(n + -5) + 1 = (n + -3) + -1(n + -2)

Reorder the terms:
2(-5 + n) + 1 = (n + -3) + -1(n + -2)
(-5 * 2 + n * 2) + 1 = (n + -3) + -1(n + -2)
(-10 + 2n) + 1 = (n + -3) + -1(n + -2)

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

Combine like terms: -10 + 1 = -9
-9 + 2n = (n + -3) + -1(n + -2)

Reorder the terms:
-9 + 2n = (-3 + n) + -1(n + -2)

Remove parenthesis around (-3 + n)
-9 + 2n = -3 + n + -1(n + -2)

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

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

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

Combine like terms: n + -1n = 0
-9 + 2n = -1 + 0
-9 + 2n = -1

Solving
-9 + 2n = -1

Solving for variable 'n'.

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

Add '9' to each side of the equation.
-9 + 9 + 2n = -1 + 9

Combine like terms: -9 + 9 = 0
0 + 2n = -1 + 9
2n = -1 + 9

Combine like terms: -1 + 9 = 8
2n = 8

Divide each side by '2'.
n = 4

Simplifying
n = 4