72=-3n+6n(3n+2)

Solution for 72=-3n+6n(3n+2) equation:

Simplifying
72 = -3n + 6n(3n + 2)

Reorder the terms:
72 = -3n + 6n(2 + 3n)
72 = -3n + (2 * 6n + 3n * 6n)
72 = -3n + (12n + 18n2)

Combine like terms: -3n + 12n = 9n
72 = 9n + 18n2

Solving
72 = 9n + 18n2

Solving for variable 'n'.

Reorder the terms:
72 + -9n + -18n2 = 9n + -9n + 18n2 + -18n2

Combine like terms: 9n + -9n = 0
72 + -9n + -18n2 = 0 + 18n2 + -18n2
72 + -9n + -18n2 = 18n2 + -18n2

Combine like terms: 18n2 + -18n2 = 0
72 + -9n + -18n2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(8 + -1n + -2n2) = 0

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

Simplifying
8 + -1n + -2n2 = 0

Solving
8 + -1n + -2n2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4 + 0.5n + n2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.5n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.5n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.5n + n2 = 0 + 4
0.5n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.5n + n2 = 4

The n term is 0.5n.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5n + 0.0625 + n2 = 4 + 0.0625

Reorder the terms:
0.0625 + 0.5n + n2 = 4 + 0.0625

Combine like terms: 4 + 0.0625 = 4.0625
0.0625 + 0.5n + n2 = 4.0625

Factor a perfect square on the left side:
(n + 0.25)(n + 0.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(n + 0.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
n + 0.25 = 2.015564437

Simplifying
n + 0.25 = 2.015564437

Reorder the terms:
0.25 + n = 2.015564437

Solving
0.25 + n = 2.015564437

Solving for variable 'n'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + n = 2.015564437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + n = 2.015564437 + -0.25
n = 2.015564437 + -0.25

Combine like terms: 2.015564437 + -0.25 = 1.765564437
n = 1.765564437

Simplifying
n = 1.765564437

Subproblem 2
n + 0.25 = -2.015564437

Simplifying
n + 0.25 = -2.015564437

Reorder the terms:
0.25 + n = -2.015564437

Solving
0.25 + n = -2.015564437

Solving for variable 'n'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + n = -2.015564437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + n = -2.015564437 + -0.25
n = -2.015564437 + -0.25

Combine like terms: -2.015564437 + -0.25 = -2.265564437
n = -2.265564437

Simplifying
n = -2.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.765564437, -2.265564437}
Solution
n = {1.765564437, -2.265564437}