7n-(1+7n)=3(n-7)-7n

Solution for 7n-(1+7n)=3(n-7)-7n equation:

Simplifying
7n + -1(1 + 7n) = 3(n + -7) + -7n
7n + (1 * -1 + 7n * -1) = 3(n + -7) + -7n
7n + (-1 + -7n) = 3(n + -7) + -7n

Reorder the terms:
-1 + 7n + -7n = 3(n + -7) + -7n

Combine like terms: 7n + -7n = 0
-1 + 0 = 3(n + -7) + -7n
-1 = 3(n + -7) + -7n

Reorder the terms:
-1 = 3(-7 + n) + -7n
-1 = (-7 * 3 + n * 3) + -7n
-1 = (-21 + 3n) + -7n

Combine like terms: 3n + -7n = -4n
-1 = -21 + -4n

Solving
-1 = -21 + -4n

Solving for variable 'n'.

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

Add '4n' to each side of the equation.
-1 + 4n = -21 + -4n + 4n

Combine like terms: -4n + 4n = 0
-1 + 4n = -21 + 0
-1 + 4n = -21

Add '1' to each side of the equation.
-1 + 1 + 4n = -21 + 1

Combine like terms: -1 + 1 = 0
0 + 4n = -21 + 1
4n = -21 + 1

Combine like terms: -21 + 1 = -20
4n = -20

Divide each side by '4'.
n = -5

Simplifying
n = -5