33=n*(n-3)

Solution for 33=n*(n-3) equation:

Simplifying
33 = n(n + -3)

Reorder the terms:
33 = n(-3 + n)
33 = (-3 * n + n * n)
33 = (-3n + n2)

Solving
33 = -3n + n2

Solving for variable 'n'.

Reorder the terms:
33 + 3n + -1n2 = -3n + 3n + n2 + -1n2

Combine like terms: -3n + 3n = 0
33 + 3n + -1n2 = 0 + n2 + -1n2
33 + 3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
33 + 3n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-33 + -3n + n2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -3n + 33 + n2 = 0 + 33

Reorder the terms:
-33 + 33 + -3n + n2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -3n + n2 = 0 + 33
-3n + n2 = 0 + 33

Combine like terms: 0 + 33 = 33
-3n + n2 = 33

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 = 33 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 33 + 2.25

Combine like terms: 33 + 2.25 = 35.25
2.25 + -3n + n2 = 35.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(n + -1.5) equal to 5.937171044 and -5.937171044.

Subproblem 1
n + -1.5 = 5.937171044

Simplifying
n + -1.5 = 5.937171044

Reorder the terms:
-1.5 + n = 5.937171044

Solving
-1.5 + n = 5.937171044

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 = 5.937171044 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 5.937171044 + 1.5
n = 5.937171044 + 1.5

Combine like terms: 5.937171044 + 1.5 = 7.437171044
n = 7.437171044

Simplifying
n = 7.437171044

Subproblem 2
n + -1.5 = -5.937171044

Simplifying
n + -1.5 = -5.937171044

Reorder the terms:
-1.5 + n = -5.937171044

Solving
-1.5 + n = -5.937171044

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 = -5.937171044 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -5.937171044 + 1.5
n = -5.937171044 + 1.5

Combine like terms: -5.937171044 + 1.5 = -4.437171044
n = -4.437171044

Simplifying
n = -4.437171044

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.437171044, -4.437171044}