3n+37=2(1+2n)+6n

Solution for 3n+37=2(1+2n)+6n equation:

Simplifying
3n + 37 = 2(1 + 2n) + 6n

Reorder the terms:
37 + 3n = 2(1 + 2n) + 6n
37 + 3n = (1 * 2 + 2n * 2) + 6n
37 + 3n = (2 + 4n) + 6n

Combine like terms: 4n + 6n = 10n
37 + 3n = 2 + 10n

Solving
37 + 3n = 2 + 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.
37 + 3n + -10n = 2 + 10n + -10n

Combine like terms: 3n + -10n = -7n
37 + -7n = 2 + 10n + -10n

Combine like terms: 10n + -10n = 0
37 + -7n = 2 + 0
37 + -7n = 2

Add '-37' to each side of the equation.
37 + -37 + -7n = 2 + -37

Combine like terms: 37 + -37 = 0
0 + -7n = 2 + -37
-7n = 2 + -37

Combine like terms: 2 + -37 = -35
-7n = -35

Divide each side by '-7'.
n = 5

Simplifying
n = 5