3n+2n(n+2)=9n+12

Solution for 3n+2n(n+2)=9n+12 equation:

Simplifying
3n + 2n(n + 2) = 9n + 12

Reorder the terms:
3n + 2n(2 + n) = 9n + 12
3n + (2 * 2n + n * 2n) = 9n + 12
3n + (4n + 2n2) = 9n + 12

Combine like terms: 3n + 4n = 7n
7n + 2n2 = 9n + 12

Reorder the terms:
7n + 2n2 = 12 + 9n

Solving
7n + 2n2 = 12 + 9n

Solving for variable 'n'.

Reorder the terms:
-12 + 7n + -9n + 2n2 = 12 + 9n + -12 + -9n

Combine like terms: 7n + -9n = -2n
-12 + -2n + 2n2 = 12 + 9n + -12 + -9n

Reorder the terms:
-12 + -2n + 2n2 = 12 + -12 + 9n + -9n

Combine like terms: 12 + -12 = 0
-12 + -2n + 2n2 = 0 + 9n + -9n
-12 + -2n + 2n2 = 9n + -9n

Combine like terms: 9n + -9n = 0
-12 + -2n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1n + n2) = 0

Factor a trinomial.
2((-2 + -1n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-2, 3}