9n^2-12=-3n

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

Simplifying
9n2 + -12 = -3n

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

Solving
-12 + 9n2 = -3n

Solving for variable 'n'.

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

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

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

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

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

Simplifying
-4 + -3n = 0

Solving
-4 + -3n = 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 + -3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3n = 0 + 4
-3n = 0 + 4

Combine like terms: 0 + 4 = 4
-3n = 4

Divide each side by '-3'.
n = -1.333333333

Simplifying
n = -1.333333333
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 = {-1.333333333, 1}