-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 = 84n
24 + 84n + -10n2 = -24 + -24n + 24 + 24n

Reorder the terms:
24 + 84n + -10n2 = -24 + 24 + -24n + 24n

Combine like terms: -24 + 24 = 0
24 + 84n + -10n2 = 0 + -24n + 24n
24 + 84n + -10n2 = -24n + 24n

Combine like terms: -24n + 24n = 0
24 + 84n + -10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 42n + -5n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + 42n + -5n2)' equal to zero and attempt to solve:

Simplifying
12 + 42n + -5n2 = 0

Solving
12 + 42n + -5n2 = 0

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

Divide each side by '-5'.
-2.4 + -8.4n + n2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -8.4n + 2.4 + n2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -8.4n + n2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -8.4n + n2 = 0 + 2.4
-8.4n + n2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-8.4n + n2 = 2.4

The n term is -8.4n.  Take half its coefficient (-4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
-8.4n + 17.64 + n2 = 2.4 + 17.64

Reorder the terms:
17.64 + -8.4n + n2 = 2.4 + 17.64

Combine like terms: 2.4 + 17.64 = 20.04
17.64 + -8.4n + n2 = 20.04

Factor a perfect square on the left side:
(n + -4.2)(n + -4.2) = 20.04

Calculate the square root of the right side: 4.476605857

Break this problem into two subproblems by setting 
(n + -4.2) equal to 4.476605857 and -4.476605857.

Subproblem 1
n + -4.2 = 4.476605857

Simplifying
n + -4.2 = 4.476605857

Reorder the terms:
-4.2 + n = 4.476605857

Solving
-4.2 + n = 4.476605857

Solving for variable 'n'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + n = 4.476605857 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + n = 4.476605857 + 4.2
n = 4.476605857 + 4.2

Combine like terms: 4.476605857 + 4.2 = 8.676605857
n = 8.676605857

Simplifying
n = 8.676605857

Subproblem 2
n + -4.2 = -4.476605857

Simplifying
n + -4.2 = -4.476605857

Reorder the terms:
-4.2 + n = -4.476605857

Solving
-4.2 + n = -4.476605857

Solving for variable 'n'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + n = -4.476605857 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + n = -4.476605857 + 4.2
n = -4.476605857 + 4.2

Combine like terms: -4.476605857 + 4.2 = -0.276605857
n = -0.276605857

Simplifying
n = -0.276605857

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.676605857, -0.276605857}
Solution
n = {8.676605857, -0.276605857}