n(n-3)=28*2

Solution for n(n-3)=28*2 equation:

Simplifying
n(n + -3) = 28 * 2

Reorder the terms:
n(-3 + n) = 28 * 2
(-3 * n + n * n) = 28 * 2
(-3n + n2) = 28 * 2

Multiply 28 * 2
-3n + n2 = 56

Solving
-3n + n2 = 56

Solving for variable 'n'.

Reorder the terms:
-56 + -3n + n2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -3n + 56 + n2 = 0 + 56

Reorder the terms:
-56 + 56 + -3n + n2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -3n + n2 = 0 + 56
-3n + n2 = 0 + 56

Combine like terms: 0 + 56 = 56
-3n + n2 = 56

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 = 56 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 56 + 2.25

Combine like terms: 56 + 2.25 = 58.25
2.25 + -3n + n2 = 58.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(n + -1.5) equal to 7.632168761 and -7.632168761.

Subproblem 1
n + -1.5 = 7.632168761

Simplifying
n + -1.5 = 7.632168761

Reorder the terms:
-1.5 + n = 7.632168761

Solving
-1.5 + n = 7.632168761

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 = 7.632168761 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 7.632168761 + 1.5
n = 7.632168761 + 1.5

Combine like terms: 7.632168761 + 1.5 = 9.132168761
n = 9.132168761

Simplifying
n = 9.132168761

Subproblem 2
n + -1.5 = -7.632168761

Simplifying
n + -1.5 = -7.632168761

Reorder the terms:
-1.5 + n = -7.632168761

Solving
-1.5 + n = -7.632168761

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 = -7.632168761 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -7.632168761 + 1.5
n = -7.632168761 + 1.5

Combine like terms: -7.632168761 + 1.5 = -6.132168761
n = -6.132168761

Simplifying
n = -6.132168761

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.132168761, -6.132168761}