12n^2-24n+10=0

Solution for 12n^2-24n+10=0 equation:

Simplifying
12n2 + -24n + 10 = 0

Reorder the terms:
10 + -24n + 12n2 = 0

Solving
10 + -24n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -12n + 6n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -12n + 6n2)' equal to zero and attempt to solve:

Simplifying
5 + -12n + 6n2 = 0

Solving
5 + -12n + 6n2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
0.8333333333 + -2n + n2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -2n + -0.8333333333 + n2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -2n + n2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -2n + n2 = 0 + -0.8333333333
-2n + n2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-2n + n2 = -0.8333333333

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = -0.8333333333 + 1

Reorder the terms:
1 + -2n + n2 = -0.8333333333 + 1

Combine like terms: -0.8333333333 + 1 = 0.1666666667
1 + -2n + n2 = 0.1666666667

Factor a perfect square on the left side:
(n + -1)(n + -1) = 0.1666666667

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(n + -1) equal to 0.408248291 and -0.408248291.

Subproblem 1
n + -1 = 0.408248291

Simplifying
n + -1 = 0.408248291

Reorder the terms:
-1 + n = 0.408248291

Solving
-1 + n = 0.408248291

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 0.408248291 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0.408248291 + 1
n = 0.408248291 + 1

Combine like terms: 0.408248291 + 1 = 1.408248291
n = 1.408248291

Simplifying
n = 1.408248291

Subproblem 2
n + -1 = -0.408248291

Simplifying
n + -1 = -0.408248291

Reorder the terms:
-1 + n = -0.408248291

Solving
-1 + n = -0.408248291

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -0.408248291 + 1

Combine like terms: -1 + 1 = 0
0 + n = -0.408248291 + 1
n = -0.408248291 + 1

Combine like terms: -0.408248291 + 1 = 0.591751709
n = 0.591751709

Simplifying
n = 0.591751709

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.408248291, 0.591751709}
Solution
n = {1.408248291, 0.591751709}