8n-6=2n(n-6)

Solution for 8n-6=2n(n-6) equation:

Simplifying
8n + -6 = 2n(n + -6)

Reorder the terms:
-6 + 8n = 2n(n + -6)

Reorder the terms:
-6 + 8n = 2n(-6 + n)
-6 + 8n = (-6 * 2n + n * 2n)
-6 + 8n = (-12n + 2n2)

Solving
-6 + 8n = -12n + 2n2

Solving for variable 'n'.

Combine like terms: 8n + 12n = 20n
-6 + 20n + -2n2 = -12n + 2n2 + 12n + -2n2

Reorder the terms:
-6 + 20n + -2n2 = -12n + 12n + 2n2 + -2n2

Combine like terms: -12n + 12n = 0
-6 + 20n + -2n2 = 0 + 2n2 + -2n2
-6 + 20n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-6 + 20n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 10n + -1n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 10n + -1n2)' equal to zero and attempt to solve:

Simplifying
-3 + 10n + -1n2 = 0

Solving
-3 + 10n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -10n + n2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -10n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + -10n + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10n + n2 = 0 + -3
-10n + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
-10n + n2 = -3

The n term is -10n.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10n + 25 + n2 = -3 + 25

Reorder the terms:
25 + -10n + n2 = -3 + 25

Combine like terms: -3 + 25 = 22
25 + -10n + n2 = 22

Factor a perfect square on the left side:
(n + -5)(n + -5) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(n + -5) equal to 4.69041576 and -4.69041576.

Subproblem 1
n + -5 = 4.69041576

Simplifying
n + -5 = 4.69041576

Reorder the terms:
-5 + n = 4.69041576

Solving
-5 + n = 4.69041576

Solving for variable 'n'.

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

Add '5' to each side of the equation.
-5 + 5 + n = 4.69041576 + 5

Combine like terms: -5 + 5 = 0
0 + n = 4.69041576 + 5
n = 4.69041576 + 5

Combine like terms: 4.69041576 + 5 = 9.69041576
n = 9.69041576

Simplifying
n = 9.69041576

Subproblem 2
n + -5 = -4.69041576

Simplifying
n + -5 = -4.69041576

Reorder the terms:
-5 + n = -4.69041576

Solving
-5 + n = -4.69041576

Solving for variable 'n'.

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

Add '5' to each side of the equation.
-5 + 5 + n = -4.69041576 + 5

Combine like terms: -5 + 5 = 0
0 + n = -4.69041576 + 5
n = -4.69041576 + 5

Combine like terms: -4.69041576 + 5 = 0.30958424
n = 0.30958424

Simplifying
n = 0.30958424

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.69041576, 0.30958424}
Solution
n = {9.69041576, 0.30958424}