6(3n+1)=8(4n+1)+1

Solution for 6(3n+1)=8(4n+1)+1 equation:

Simplifying
6(3n + 1) = 8(4n + 1) + 1

Reorder the terms:
6(1 + 3n) = 8(4n + 1) + 1
(1 * 6 + 3n * 6) = 8(4n + 1) + 1
(6 + 18n) = 8(4n + 1) + 1

Reorder the terms:
6 + 18n = 8(1 + 4n) + 1
6 + 18n = (1 * 8 + 4n * 8) + 1
6 + 18n = (8 + 32n) + 1

Reorder the terms:
6 + 18n = 8 + 1 + 32n

Combine like terms: 8 + 1 = 9
6 + 18n = 9 + 32n

Solving
6 + 18n = 9 + 32n

Solving for variable 'n'.

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

Add '-32n' to each side of the equation.
6 + 18n + -32n = 9 + 32n + -32n

Combine like terms: 18n + -32n = -14n
6 + -14n = 9 + 32n + -32n

Combine like terms: 32n + -32n = 0
6 + -14n = 9 + 0
6 + -14n = 9

Add '-6' to each side of the equation.
6 + -6 + -14n = 9 + -6

Combine like terms: 6 + -6 = 0
0 + -14n = 9 + -6
-14n = 9 + -6

Combine like terms: 9 + -6 = 3
-14n = 3

Divide each side by '-14'.
n = -0.2142857143

Simplifying
n = -0.2142857143