12n^2-32n=-16

Solution for 12n^2-32n=-16 equation:

Simplifying
12n2 + -32n = -16

Reorder the terms:
-32n + 12n2 = -16

Solving
-32n + 12n2 = -16

Solving for variable 'n'.

Reorder the terms:
16 + -32n + 12n2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -32n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -8n + 3n2) = 0

Factor a trinomial.
4((2 + -3n)(2 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

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

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

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

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Subproblem 2
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
Solution
n = {0.6666666667, 2}