-6+3(2n+7)=3(6n+1)-8n

Solution for -6+3(2n+7)=3(6n+1)-8n equation:

Simplifying
-6 + 3(2n + 7) = 3(6n + 1) + -8n

Reorder the terms:
-6 + 3(7 + 2n) = 3(6n + 1) + -8n
-6 + (7 * 3 + 2n * 3) = 3(6n + 1) + -8n
-6 + (21 + 6n) = 3(6n + 1) + -8n

Combine like terms: -6 + 21 = 15
15 + 6n = 3(6n + 1) + -8n

Reorder the terms:
15 + 6n = 3(1 + 6n) + -8n
15 + 6n = (1 * 3 + 6n * 3) + -8n
15 + 6n = (3 + 18n) + -8n

Combine like terms: 18n + -8n = 10n
15 + 6n = 3 + 10n

Solving
15 + 6n = 3 + 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.
15 + 6n + -10n = 3 + 10n + -10n

Combine like terms: 6n + -10n = -4n
15 + -4n = 3 + 10n + -10n

Combine like terms: 10n + -10n = 0
15 + -4n = 3 + 0
15 + -4n = 3

Add '-15' to each side of the equation.
15 + -15 + -4n = 3 + -15

Combine like terms: 15 + -15 = 0
0 + -4n = 3 + -15
-4n = 3 + -15

Combine like terms: 3 + -15 = -12
-4n = -12

Divide each side by '-4'.
n = 3

Simplifying
n = 3