83=3(1+7n)-5n

Solution for 83=3(1+7n)-5n equation:

Simplifying
83 = 3(1 + 7n) + -5n
83 = (1 * 3 + 7n * 3) + -5n
83 = (3 + 21n) + -5n

Combine like terms: 21n + -5n = 16n
83 = 3 + 16n

Solving
83 = 3 + 16n

Solving for variable 'n'.

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

Add '-16n' to each side of the equation.
83 + -16n = 3 + 16n + -16n

Combine like terms: 16n + -16n = 0
83 + -16n = 3 + 0
83 + -16n = 3

Add '-83' to each side of the equation.
83 + -83 + -16n = 3 + -83

Combine like terms: 83 + -83 = 0
0 + -16n = 3 + -83
-16n = 3 + -83

Combine like terms: 3 + -83 = -80
-16n = -80

Divide each side by '-16'.
n = 5

Simplifying
n = 5