(3n+1)(n+2)=12

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

Simplifying
(3n + 1)(n + 2) = 12

Reorder the terms:
(1 + 3n)(n + 2) = 12

Reorder the terms:
(1 + 3n)(2 + n) = 12

Multiply (1 + 3n) * (2 + n)
(1(2 + n) + 3n * (2 + n)) = 12
((2 * 1 + n * 1) + 3n * (2 + n)) = 12
((2 + 1n) + 3n * (2 + n)) = 12
(2 + 1n + (2 * 3n + n * 3n)) = 12
(2 + 1n + (6n + 3n2)) = 12

Combine like terms: 1n + 6n = 7n
(2 + 7n + 3n2) = 12

Solving
2 + 7n + 3n2 = 12

Solving for variable 'n'.

Reorder the terms:
2 + -12 + 7n + 3n2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 7n + 3n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 7n + 3n2 = 0

Factor a trinomial.
(-10 + -3n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-10 + -3n)' equal to zero and attempt to solve:

Simplifying
-10 + -3n = 0

Solving
-10 + -3n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3n = 0 + 10

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

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

Divide each side by '-3'.
n = -3.333333333

Simplifying
n = -3.333333333
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-3.333333333, 1}