3(2n-9)=2(5n+6)+1

Solution for 3(2n-9)=2(5n+6)+1 equation:

Simplifying
3(2n + -9) = 2(5n + 6) + 1

Reorder the terms:
3(-9 + 2n) = 2(5n + 6) + 1
(-9 * 3 + 2n * 3) = 2(5n + 6) + 1
(-27 + 6n) = 2(5n + 6) + 1

Reorder the terms:
-27 + 6n = 2(6 + 5n) + 1
-27 + 6n = (6 * 2 + 5n * 2) + 1
-27 + 6n = (12 + 10n) + 1

Reorder the terms:
-27 + 6n = 12 + 1 + 10n

Combine like terms: 12 + 1 = 13
-27 + 6n = 13 + 10n

Solving
-27 + 6n = 13 + 10n

Solving for variable 'n'.

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

Add '-10n' to each side of the equation.
-27 + 6n + -10n = 13 + 10n + -10n

Combine like terms: 6n + -10n = -4n
-27 + -4n = 13 + 10n + -10n

Combine like terms: 10n + -10n = 0
-27 + -4n = 13 + 0
-27 + -4n = 13

Add '27' to each side of the equation.
-27 + 27 + -4n = 13 + 27

Combine like terms: -27 + 27 = 0
0 + -4n = 13 + 27
-4n = 13 + 27

Combine like terms: 13 + 27 = 40
-4n = 40

Divide each side by '-4'.
n = -10

Simplifying
n = -10