6(n-6)2n=10

Solution for 6(n-6)2n=10 equation:

Simplifying
6(n + -6) * 2n = 10

Reorder the terms:
6(-6 + n) * 2n = 10

Reorder the terms for easier multiplication:
6 * 2n(-6 + n) = 10

Multiply 6 * 2
12n(-6 + n) = 10
(-6 * 12n + n * 12n) = 10
(-72n + 12n2) = 10

Solving
-72n + 12n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -72n + 12n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -72n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -36n + 6n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -36n + 6n2)' equal to zero and attempt to solve:

Simplifying
-5 + -36n + 6n2 = 0

Solving
-5 + -36n + 6n2 = 0

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

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

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -6n + 0.8333333333 + n2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -6n + n2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -6n + n2 = 0 + 0.8333333333
-6n + n2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-6n + n2 = 0.8333333333

The n term is -6n.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6n + 9 + n2 = 0.8333333333 + 9

Reorder the terms:
9 + -6n + n2 = 0.8333333333 + 9

Combine like terms: 0.8333333333 + 9 = 9.8333333333
9 + -6n + n2 = 9.8333333333

Factor a perfect square on the left side:
(n + -3)(n + -3) = 9.8333333333

Calculate the square root of the right side: 3.13581462

Break this problem into two subproblems by setting 
(n + -3) equal to 3.13581462 and -3.13581462.

Subproblem 1
n + -3 = 3.13581462

Simplifying
n + -3 = 3.13581462

Reorder the terms:
-3 + n = 3.13581462

Solving
-3 + n = 3.13581462

Solving for variable 'n'.

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

Add '3' to each side of the equation.
-3 + 3 + n = 3.13581462 + 3

Combine like terms: -3 + 3 = 0
0 + n = 3.13581462 + 3
n = 3.13581462 + 3

Combine like terms: 3.13581462 + 3 = 6.13581462
n = 6.13581462

Simplifying
n = 6.13581462

Subproblem 2
n + -3 = -3.13581462

Simplifying
n + -3 = -3.13581462

Reorder the terms:
-3 + n = -3.13581462

Solving
-3 + n = -3.13581462

Solving for variable 'n'.

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

Add '3' to each side of the equation.
-3 + 3 + n = -3.13581462 + 3

Combine like terms: -3 + 3 = 0
0 + n = -3.13581462 + 3
n = -3.13581462 + 3

Combine like terms: -3.13581462 + 3 = -0.13581462
n = -0.13581462

Simplifying
n = -0.13581462

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.13581462, -0.13581462}
Solution
n = {6.13581462, -0.13581462}