2n+1+1+6n=6(n-5)+8(1+n)

Solution for 2n+1+1+6n=6(n-5)+8(1+n) equation:

Simplifying
2n + 1 + 1 + 6n = 6(n + -5) + 8(1 + n)

Reorder the terms:
1 + 1 + 2n + 6n = 6(n + -5) + 8(1 + n)

Combine like terms: 1 + 1 = 2
2 + 2n + 6n = 6(n + -5) + 8(1 + n)

Combine like terms: 2n + 6n = 8n
2 + 8n = 6(n + -5) + 8(1 + n)

Reorder the terms:
2 + 8n = 6(-5 + n) + 8(1 + n)
2 + 8n = (-5 * 6 + n * 6) + 8(1 + n)
2 + 8n = (-30 + 6n) + 8(1 + n)
2 + 8n = -30 + 6n + (1 * 8 + n * 8)
2 + 8n = -30 + 6n + (8 + 8n)

Reorder the terms:
2 + 8n = -30 + 8 + 6n + 8n

Combine like terms: -30 + 8 = -22
2 + 8n = -22 + 6n + 8n

Combine like terms: 6n + 8n = 14n
2 + 8n = -22 + 14n

Solving
2 + 8n = -22 + 14n

Solving for variable 'n'.

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

Add '-14n' to each side of the equation.
2 + 8n + -14n = -22 + 14n + -14n

Combine like terms: 8n + -14n = -6n
2 + -6n = -22 + 14n + -14n

Combine like terms: 14n + -14n = 0
2 + -6n = -22 + 0
2 + -6n = -22

Add '-2' to each side of the equation.
2 + -2 + -6n = -22 + -2

Combine like terms: 2 + -2 = 0
0 + -6n = -22 + -2
-6n = -22 + -2

Combine like terms: -22 + -2 = -24
-6n = -24

Divide each side by '-6'.
n = 4

Simplifying
n = 4