6(2n+4)2n=-3(1-2n)-13

Solution for 6(2n+4)2n=-3(1-2n)-13 equation:

Simplifying
6(2n + 4) * 2n = -3(1 + -2n) + -13

Reorder the terms:
6(4 + 2n) * 2n = -3(1 + -2n) + -13

Reorder the terms for easier multiplication:
6 * 2n(4 + 2n) = -3(1 + -2n) + -13

Multiply 6 * 2
12n(4 + 2n) = -3(1 + -2n) + -13
(4 * 12n + 2n * 12n) = -3(1 + -2n) + -13
(48n + 24n2) = -3(1 + -2n) + -13
48n + 24n2 = (1 * -3 + -2n * -3) + -13
48n + 24n2 = (-3 + 6n) + -13

Reorder the terms:
48n + 24n2 = -3 + -13 + 6n

Combine like terms: -3 + -13 = -16
48n + 24n2 = -16 + 6n

Solving
48n + 24n2 = -16 + 6n

Solving for variable 'n'.

Reorder the terms:
16 + 48n + -6n + 24n2 = -16 + 6n + 16 + -6n

Combine like terms: 48n + -6n = 42n
16 + 42n + 24n2 = -16 + 6n + 16 + -6n

Reorder the terms:
16 + 42n + 24n2 = -16 + 16 + 6n + -6n

Combine like terms: -16 + 16 = 0
16 + 42n + 24n2 = 0 + 6n + -6n
16 + 42n + 24n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
16 + 42n + 24n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 21n + 12n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 21n + 12n2)' equal to zero and attempt to solve:

Simplifying
8 + 21n + 12n2 = 0

Solving
8 + 21n + 12n2 = 0

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

Divide each side by '12'.
0.6666666667 + 1.75n + n2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 1.75n + -0.6666666667 + n2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 1.75n + n2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 1.75n + n2 = 0 + -0.6666666667
1.75n + n2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
1.75n + n2 = -0.6666666667

The n term is 1.75n.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75n + 0.765625 + n2 = -0.6666666667 + 0.765625

Reorder the terms:
0.765625 + 1.75n + n2 = -0.6666666667 + 0.765625

Combine like terms: -0.6666666667 + 0.765625 = 0.0989583333
0.765625 + 1.75n + n2 = 0.0989583333

Factor a perfect square on the left side:
(n + 0.875)(n + 0.875) = 0.0989583333

Calculate the square root of the right side: 0.314576435

Break this problem into two subproblems by setting 
(n + 0.875) equal to 0.314576435 and -0.314576435.

Subproblem 1
n + 0.875 = 0.314576435

Simplifying
n + 0.875 = 0.314576435

Reorder the terms:
0.875 + n = 0.314576435

Solving
0.875 + n = 0.314576435

Solving for variable 'n'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + n = 0.314576435 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + n = 0.314576435 + -0.875
n = 0.314576435 + -0.875

Combine like terms: 0.314576435 + -0.875 = -0.560423565
n = -0.560423565

Simplifying
n = -0.560423565

Subproblem 2
n + 0.875 = -0.314576435

Simplifying
n + 0.875 = -0.314576435

Reorder the terms:
0.875 + n = -0.314576435

Solving
0.875 + n = -0.314576435

Solving for variable 'n'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + n = -0.314576435 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + n = -0.314576435 + -0.875
n = -0.314576435 + -0.875

Combine like terms: -0.314576435 + -0.875 = -1.189576435
n = -1.189576435

Simplifying
n = -1.189576435

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.560423565, -1.189576435}
Solution
n = {-0.560423565, -1.189576435}