6(3n+1)=9(5n+8)+3

Solution for 6(3n+1)=9(5n+8)+3 equation:

Simplifying
6(3n + 1) = 9(5n + 8) + 3

Reorder the terms:
6(1 + 3n) = 9(5n + 8) + 3
(1 * 6 + 3n * 6) = 9(5n + 8) + 3
(6 + 18n) = 9(5n + 8) + 3

Reorder the terms:
6 + 18n = 9(8 + 5n) + 3
6 + 18n = (8 * 9 + 5n * 9) + 3
6 + 18n = (72 + 45n) + 3

Reorder the terms:
6 + 18n = 72 + 3 + 45n

Combine like terms: 72 + 3 = 75
6 + 18n = 75 + 45n

Solving
6 + 18n = 75 + 45n

Solving for variable 'n'.

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

Add '-45n' to each side of the equation.
6 + 18n + -45n = 75 + 45n + -45n

Combine like terms: 18n + -45n = -27n
6 + -27n = 75 + 45n + -45n

Combine like terms: 45n + -45n = 0
6 + -27n = 75 + 0
6 + -27n = 75

Add '-6' to each side of the equation.
6 + -6 + -27n = 75 + -6

Combine like terms: 6 + -6 = 0
0 + -27n = 75 + -6
-27n = 75 + -6

Combine like terms: 75 + -6 = 69
-27n = 69

Divide each side by '-27'.
n = -2.555555556

Simplifying
n = -2.555555556