6(3n+1)=7(5n+1)+8

Solution for 6(3n+1)=7(5n+1)+8 equation:

Simplifying
6(3n + 1) = 7(5n + 1) + 8

Reorder the terms:
6(1 + 3n) = 7(5n + 1) + 8
(1 * 6 + 3n * 6) = 7(5n + 1) + 8
(6 + 18n) = 7(5n + 1) + 8

Reorder the terms:
6 + 18n = 7(1 + 5n) + 8
6 + 18n = (1 * 7 + 5n * 7) + 8
6 + 18n = (7 + 35n) + 8

Reorder the terms:
6 + 18n = 7 + 8 + 35n

Combine like terms: 7 + 8 = 15
6 + 18n = 15 + 35n

Solving
6 + 18n = 15 + 35n

Solving for variable 'n'.

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

Add '-35n' to each side of the equation.
6 + 18n + -35n = 15 + 35n + -35n

Combine like terms: 18n + -35n = -17n
6 + -17n = 15 + 35n + -35n

Combine like terms: 35n + -35n = 0
6 + -17n = 15 + 0
6 + -17n = 15

Add '-6' to each side of the equation.
6 + -6 + -17n = 15 + -6

Combine like terms: 6 + -6 = 0
0 + -17n = 15 + -6
-17n = 15 + -6

Combine like terms: 15 + -6 = 9
-17n = 9

Divide each side by '-17'.
n = -0.5294117647

Simplifying
n = -0.5294117647