-4n(n+6)-(1+2n)=

Solution for -4n(n+6)-(1+2n)= equation:

Simplifying
-4n(n + 6) + -1(1 + 2n) = 0

Reorder the terms:
-4n(6 + n) + -1(1 + 2n) = 0
(6 * -4n + n * -4n) + -1(1 + 2n) = 0
(-24n + -4n2) + -1(1 + 2n) = 0
-24n + -4n2 + (1 * -1 + 2n * -1) = 0
-24n + -4n2 + (-1 + -2n) = 0

Reorder the terms:
-1 + -24n + -2n + -4n2 = 0

Combine like terms: -24n + -2n = -26n
-1 + -26n + -4n2 = 0

Solving
-1 + -26n + -4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 26n + 4n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 26n + 4n2)' equal to zero and attempt to solve:

Simplifying
1 + 26n + 4n2 = 0

Solving
1 + 26n + 4n2 = 0

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

Divide each side by '4'.
0.25 + 6.5n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 6.5n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 6.5n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 6.5n + n2 = 0 + -0.25
6.5n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
6.5n + n2 = -0.25

The n term is 6.5n.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5n + 10.5625 + n2 = -0.25 + 10.5625

Reorder the terms:
10.5625 + 6.5n + n2 = -0.25 + 10.5625

Combine like terms: -0.25 + 10.5625 = 10.3125
10.5625 + 6.5n + n2 = 10.3125

Factor a perfect square on the left side:
(n + 3.25)(n + 3.25) = 10.3125

Calculate the square root of the right side: 3.211308145

Break this problem into two subproblems by setting 
(n + 3.25) equal to 3.211308145 and -3.211308145.

Subproblem 1
n + 3.25 = 3.211308145

Simplifying
n + 3.25 = 3.211308145

Reorder the terms:
3.25 + n = 3.211308145

Solving
3.25 + n = 3.211308145

Solving for variable 'n'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + n = 3.211308145 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + n = 3.211308145 + -3.25
n = 3.211308145 + -3.25

Combine like terms: 3.211308145 + -3.25 = -0.038691855
n = -0.038691855

Simplifying
n = -0.038691855

Subproblem 2
n + 3.25 = -3.211308145

Simplifying
n + 3.25 = -3.211308145

Reorder the terms:
3.25 + n = -3.211308145

Solving
3.25 + n = -3.211308145

Solving for variable 'n'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + n = -3.211308145 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + n = -3.211308145 + -3.25
n = -3.211308145 + -3.25

Combine like terms: -3.211308145 + -3.25 = -6.461308145
n = -6.461308145

Simplifying
n = -6.461308145

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.038691855, -6.461308145}
Solution
n = {-0.038691855, -6.461308145}