n(n-3)=28*128

Solution for n(n-3)=28*128 equation:

Simplifying
n(n + -3) = 28 * 128

Reorder the terms:
n(-3 + n) = 28 * 128
(-3 * n + n * n) = 28 * 128
(-3n + n2) = 28 * 128

Multiply 28 * 128
-3n + n2 = 3584

Solving
-3n + n2 = 3584

Solving for variable 'n'.

Reorder the terms:
-3584 + -3n + n2 = 3584 + -3584

Combine like terms: 3584 + -3584 = 0
-3584 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3584' to each side of the equation.
-3584 + -3n + 3584 + n2 = 0 + 3584

Reorder the terms:
-3584 + 3584 + -3n + n2 = 0 + 3584

Combine like terms: -3584 + 3584 = 0
0 + -3n + n2 = 0 + 3584
-3n + n2 = 0 + 3584

Combine like terms: 0 + 3584 = 3584
-3n + n2 = 3584

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 3584 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 3584 + 2.25

Combine like terms: 3584 + 2.25 = 3586.25
2.25 + -3n + n2 = 3586.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 3586.25

Calculate the square root of the right side: 59.885307046

Break this problem into two subproblems by setting 
(n + -1.5) equal to 59.885307046 and -59.885307046.

Subproblem 1
n + -1.5 = 59.885307046

Simplifying
n + -1.5 = 59.885307046

Reorder the terms:
-1.5 + n = 59.885307046

Solving
-1.5 + n = 59.885307046

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 59.885307046 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 59.885307046 + 1.5
n = 59.885307046 + 1.5

Combine like terms: 59.885307046 + 1.5 = 61.385307046
n = 61.385307046

Simplifying
n = 61.385307046

Subproblem 2
n + -1.5 = -59.885307046

Simplifying
n + -1.5 = -59.885307046

Reorder the terms:
-1.5 + n = -59.885307046

Solving
-1.5 + n = -59.885307046

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -59.885307046 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -59.885307046 + 1.5
n = -59.885307046 + 1.5

Combine like terms: -59.885307046 + 1.5 = -58.385307046
n = -58.385307046

Simplifying
n = -58.385307046

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {61.385307046, -58.385307046}