3n^2+9n=12

Solution for 3n^2+9n=12 equation:

Simplifying
3n2 + 9n = 12

Reorder the terms:
9n + 3n2 = 12

Solving
9n + 3n2 = 12

Solving for variable 'n'.

Reorder the terms:
-12 + 9n + 3n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 9n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 3n + n2) = 0

Factor a trinomial.
3((-4 + -1n)(1 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
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 = {-4, 1}