3n^2-12n=-9

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

Simplifying
3n2 + -12n = -9

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

Solving
-12n + 3n2 = -9

Solving for variable 'n'.

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

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

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

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

Ignore the factor 3.
Subproblem 1
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
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 = {1, 3}