3(1+3n)+2(5-4n)=12

Solution for 3(1+3n)+2(5-4n)=12 equation:

Simplifying
3(1 + 3n) + 2(5 + -4n) = 12
(1 * 3 + 3n * 3) + 2(5 + -4n) = 12
(3 + 9n) + 2(5 + -4n) = 12
3 + 9n + (5 * 2 + -4n * 2) = 12
3 + 9n + (10 + -8n) = 12

Reorder the terms:
3 + 10 + 9n + -8n = 12

Combine like terms: 3 + 10 = 13
13 + 9n + -8n = 12

Combine like terms: 9n + -8n = 1n
13 + 1n = 12

Solving
13 + 1n = 12

Solving for variable 'n'.

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

Add '-13' to each side of the equation.
13 + -13 + 1n = 12 + -13

Combine like terms: 13 + -13 = 0
0 + 1n = 12 + -13
1n = 12 + -13

Combine like terms: 12 + -13 = -1
1n = -1

Divide each side by '1'.
n = -1

Simplifying
n = -1