0=0.12(n-10)(2n+4)

Solution for 0=0.12(n-10)(2n+4) equation:

Simplifying
0 = 0.12(n + -10)(2n + 4)

Reorder the terms:
0 = 0.12(-10 + n)(2n + 4)

Reorder the terms:
0 = 0.12(-10 + n)(4 + 2n)

Multiply (-10 + n) * (4 + 2n)
0 = 0.12(-10(4 + 2n) + n(4 + 2n))
0 = 0.12((4 * -10 + 2n * -10) + n(4 + 2n))
0 = 0.12((-40 + -20n) + n(4 + 2n))
0 = 0.12(-40 + -20n + (4 * n + 2n * n))
0 = 0.12(-40 + -20n + (4n + 2n2))

Combine like terms: -20n + 4n = -16n
0 = 0.12(-40 + -16n + 2n2)
0 = (-40 * 0.12 + -16n * 0.12 + 2n2 * 0.12)
0 = (-4.8 + -1.92n + 0.24n2)

Solving
0 = -4.8 + -1.92n + 0.24n2

Solving for variable 'n'.

Combine like terms: 0 + 4.8 = 4.8
4.8 + 1.92n + -0.24n2 = -4.8 + -1.92n + 0.24n2 + 4.8 + 1.92n + -0.24n2

Reorder the terms:
4.8 + 1.92n + -0.24n2 = -4.8 + 4.8 + -1.92n + 1.92n + 0.24n2 + -0.24n2

Combine like terms: -4.8 + 4.8 = 0.0
4.8 + 1.92n + -0.24n2 = 0.0 + -1.92n + 1.92n + 0.24n2 + -0.24n2
4.8 + 1.92n + -0.24n2 = -1.92n + 1.92n + 0.24n2 + -0.24n2

Combine like terms: -1.92n + 1.92n = 0.00
4.8 + 1.92n + -0.24n2 = 0.00 + 0.24n2 + -0.24n2
4.8 + 1.92n + -0.24n2 = 0.24n2 + -0.24n2

Combine like terms: 0.24n2 + -0.24n2 = 0.00
4.8 + 1.92n + -0.24n2 = 0.00

Begin completing the square.  Divide all terms by
-0.24 the coefficient of the squared term: 

Divide each side by '-0.24'.
-20 + -8n + n2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -8n + 20 + n2 = 0 + 20

Reorder the terms:
-20 + 20 + -8n + n2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -8n + n2 = 0 + 20
-8n + n2 = 0 + 20

Combine like terms: 0 + 20 = 20
-8n + n2 = 20

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = 20 + 16

Reorder the terms:
16 + -8n + n2 = 20 + 16

Combine like terms: 20 + 16 = 36
16 + -8n + n2 = 36

Factor a perfect square on the left side:
(n + -4)(n + -4) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(n + -4) equal to 6 and -6.

Subproblem 1
n + -4 = 6

Simplifying
n + -4 = 6

Reorder the terms:
-4 + n = 6

Solving
-4 + n = 6

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = 6 + 4

Combine like terms: -4 + 4 = 0
0 + n = 6 + 4
n = 6 + 4

Combine like terms: 6 + 4 = 10
n = 10

Simplifying
n = 10

Subproblem 2
n + -4 = -6

Simplifying
n + -4 = -6

Reorder the terms:
-4 + n = -6

Solving
-4 + n = -6

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = -6 + 4

Combine like terms: -4 + 4 = 0
0 + n = -6 + 4
n = -6 + 4

Combine like terms: -6 + 4 = -2
n = -2

Simplifying
n = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10, -2}