12n^2-9=12n

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

Simplifying
12n2 + -9 = 12n

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

Solving
-9 + 12n2 = 12n

Solving for variable 'n'.

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

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

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

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

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 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 + -2n = 0 + 1

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

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

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-0.5, 1.5}