10n(n-6)=-4(6n+6)

Solution for 10n(n-6)=-4(6n+6) equation:

Simplifying
10n(n + -6) = -4(6n + 6)

Reorder the terms:
10n(-6 + n) = -4(6n + 6)
(-6 * 10n + n * 10n) = -4(6n + 6)
(-60n + 10n2) = -4(6n + 6)

Reorder the terms:
-60n + 10n2 = -4(6 + 6n)
-60n + 10n2 = (6 * -4 + 6n * -4)
-60n + 10n2 = (-24 + -24n)

Solving
-60n + 10n2 = -24 + -24n

Solving for variable 'n'.

Reorder the terms:
24 + -60n + 24n + 10n2 = -24 + -24n + 24 + 24n

Combine like terms: -60n + 24n = -36n
24 + -36n + 10n2 = -24 + -24n + 24 + 24n

Reorder the terms:
24 + -36n + 10n2 = -24 + 24 + -24n + 24n

Combine like terms: -24 + 24 = 0
24 + -36n + 10n2 = 0 + -24n + 24n
24 + -36n + 10n2 = -24n + 24n

Combine like terms: -24n + 24n = 0
24 + -36n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -18n + 5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + -18n + 5n2)' equal to zero and attempt to solve:

Simplifying
12 + -18n + 5n2 = 0

Solving
12 + -18n + 5n2 = 0

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

Divide each side by '5'.
2.4 + -3.6n + n2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -3.6n + -2.4 + n2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -3.6n + n2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -3.6n + n2 = 0 + -2.4
-3.6n + n2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-3.6n + n2 = -2.4

The n term is -3.6n.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6n + 3.24 + n2 = -2.4 + 3.24

Reorder the terms:
3.24 + -3.6n + n2 = -2.4 + 3.24

Combine like terms: -2.4 + 3.24 = 0.84
3.24 + -3.6n + n2 = 0.84

Factor a perfect square on the left side:
(n + -1.8)(n + -1.8) = 0.84

Calculate the square root of the right side: 0.916515139

Break this problem into two subproblems by setting 
(n + -1.8) equal to 0.916515139 and -0.916515139.

Subproblem 1
n + -1.8 = 0.916515139

Simplifying
n + -1.8 = 0.916515139

Reorder the terms:
-1.8 + n = 0.916515139

Solving
-1.8 + n = 0.916515139

Solving for variable 'n'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + n = 0.916515139 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + n = 0.916515139 + 1.8
n = 0.916515139 + 1.8

Combine like terms: 0.916515139 + 1.8 = 2.716515139
n = 2.716515139

Simplifying
n = 2.716515139

Subproblem 2
n + -1.8 = -0.916515139

Simplifying
n + -1.8 = -0.916515139

Reorder the terms:
-1.8 + n = -0.916515139

Solving
-1.8 + n = -0.916515139

Solving for variable 'n'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + n = -0.916515139 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + n = -0.916515139 + 1.8
n = -0.916515139 + 1.8

Combine like terms: -0.916515139 + 1.8 = 0.883484861
n = 0.883484861

Simplifying
n = 0.883484861

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.716515139, 0.883484861}
Solution
n = {2.716515139, 0.883484861}