-2n(-8n-10)-6(-10n-3)=

Solution for -2n(-8n-10)-6(-10n-3)= equation:

Simplifying
-2n(-8n + -10) + -6(-10n + -3) = 0

Reorder the terms:
-2n(-10 + -8n) + -6(-10n + -3) = 0
(-10 * -2n + -8n * -2n) + -6(-10n + -3) = 0
(20n + 16n2) + -6(-10n + -3) = 0

Reorder the terms:
20n + 16n2 + -6(-3 + -10n) = 0
20n + 16n2 + (-3 * -6 + -10n * -6) = 0
20n + 16n2 + (18 + 60n) = 0

Reorder the terms:
18 + 20n + 60n + 16n2 = 0

Combine like terms: 20n + 60n = 80n
18 + 80n + 16n2 = 0

Solving
18 + 80n + 16n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 40n + 8n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + 40n + 8n2)' equal to zero and attempt to solve:

Simplifying
9 + 40n + 8n2 = 0

Solving
9 + 40n + 8n2 = 0

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

Divide each side by '8'.
1.125 + 5n + n2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + 5n + -1.125 + n2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + 5n + n2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + 5n + n2 = 0 + -1.125
5n + n2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
5n + n2 = -1.125

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = -1.125 + 6.25

Reorder the terms:
6.25 + 5n + n2 = -1.125 + 6.25

Combine like terms: -1.125 + 6.25 = 5.125
6.25 + 5n + n2 = 5.125

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 5.125

Calculate the square root of the right side: 2.263846285

Break this problem into two subproblems by setting 
(n + 2.5) equal to 2.263846285 and -2.263846285.

Subproblem 1
n + 2.5 = 2.263846285

Simplifying
n + 2.5 = 2.263846285

Reorder the terms:
2.5 + n = 2.263846285

Solving
2.5 + n = 2.263846285

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = 2.263846285 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 2.263846285 + -2.5
n = 2.263846285 + -2.5

Combine like terms: 2.263846285 + -2.5 = -0.236153715
n = -0.236153715

Simplifying
n = -0.236153715

Subproblem 2
n + 2.5 = -2.263846285

Simplifying
n + 2.5 = -2.263846285

Reorder the terms:
2.5 + n = -2.263846285

Solving
2.5 + n = -2.263846285

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = -2.263846285 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -2.263846285 + -2.5
n = -2.263846285 + -2.5

Combine like terms: -2.263846285 + -2.5 = -4.763846285
n = -4.763846285

Simplifying
n = -4.763846285

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.236153715, -4.763846285}
Solution
n = {-0.236153715, -4.763846285}