6n^2-12n=10

Solution for 6n^2-12n=10 equation:

Simplifying
6n2 + -12n = 10

Reorder the terms:
-12n + 6n2 = 10

Solving
-12n + 6n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -12n + 6n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -12n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -6n + 3n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -6n + 3n2)' equal to zero and attempt to solve:

Simplifying
-5 + -6n + 3n2 = 0

Solving
-5 + -6n + 3n2 = 0

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

Divide each side by '3'.
-1.666666667 + -2n + n2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2n + 1.666666667 + n2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2n + n2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2n + n2 = 0 + 1.666666667
-2n + n2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2n + n2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + -2n + n2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + -2n + n2 = 2.666666667

Factor a perfect square on the left side:
(n + -1)(n + -1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(n + -1) equal to 1.632993162 and -1.632993162.

Subproblem 1
n + -1 = 1.632993162

Simplifying
n + -1 = 1.632993162

Reorder the terms:
-1 + n = 1.632993162

Solving
-1 + n = 1.632993162

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 = 1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + n = 1.632993162 + 1
n = 1.632993162 + 1

Combine like terms: 1.632993162 + 1 = 2.632993162
n = 2.632993162

Simplifying
n = 2.632993162

Subproblem 2
n + -1 = -1.632993162

Simplifying
n + -1 = -1.632993162

Reorder the terms:
-1 + n = -1.632993162

Solving
-1 + n = -1.632993162

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 = -1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + n = -1.632993162 + 1
n = -1.632993162 + 1

Combine like terms: -1.632993162 + 1 = -0.632993162
n = -0.632993162

Simplifying
n = -0.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.632993162, -0.632993162}
Solution
n = {2.632993162, -0.632993162}