6(n-3)2n=10

Solution for 6(n-3)2n=10 equation:

Simplifying
6(n + -3) * 2n = 10

Reorder the terms:
6(-3 + n) * 2n = 10

Reorder the terms for easier multiplication:
6 * 2n(-3 + n) = 10

Multiply 6 * 2
12n(-3 + n) = 10
(-3 * 12n + n * 12n) = 10
(-36n + 12n2) = 10

Solving
-36n + 12n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -36n + 12n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -36n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -18n + 6n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -18n + 6n2)' equal to zero and attempt to solve:

Simplifying
-5 + -18n + 6n2 = 0

Solving
-5 + -18n + 6n2 = 0

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

Divide each side by '6'.
-0.8333333333 + -3n + n2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -3n + 0.8333333333 + n2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -3n + n2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -3n + n2 = 0 + 0.8333333333
-3n + n2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-3n + n2 = 0.8333333333

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 0.8333333333 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 0.8333333333 + 2.25

Combine like terms: 0.8333333333 + 2.25 = 3.0833333333
2.25 + -3n + n2 = 3.0833333333

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 3.0833333333

Calculate the square root of the right side: 1.755942292

Break this problem into two subproblems by setting 
(n + -1.5) equal to 1.755942292 and -1.755942292.

Subproblem 1
n + -1.5 = 1.755942292

Simplifying
n + -1.5 = 1.755942292

Reorder the terms:
-1.5 + n = 1.755942292

Solving
-1.5 + n = 1.755942292

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 1.755942292 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 1.755942292 + 1.5
n = 1.755942292 + 1.5

Combine like terms: 1.755942292 + 1.5 = 3.255942292
n = 3.255942292

Simplifying
n = 3.255942292

Subproblem 2
n + -1.5 = -1.755942292

Simplifying
n + -1.5 = -1.755942292

Reorder the terms:
-1.5 + n = -1.755942292

Solving
-1.5 + n = -1.755942292

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -1.755942292 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -1.755942292 + 1.5
n = -1.755942292 + 1.5

Combine like terms: -1.755942292 + 1.5 = -0.255942292
n = -0.255942292

Simplifying
n = -0.255942292

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.255942292, -0.255942292}
Solution
n = {3.255942292, -0.255942292}