5n^2-36n+57=0

Solution for 5n^2-36n+57=0 equation:

Simplifying
5n2 + -36n + 57 = 0

Reorder the terms:
57 + -36n + 5n2 = 0

Solving
57 + -36n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
11.4 + -7.2n + n2 = 0

Move the constant term to the right:

Add '-11.4' to each side of the equation.
11.4 + -7.2n + -11.4 + n2 = 0 + -11.4

Reorder the terms:
11.4 + -11.4 + -7.2n + n2 = 0 + -11.4

Combine like terms: 11.4 + -11.4 = 0.0
0.0 + -7.2n + n2 = 0 + -11.4
-7.2n + n2 = 0 + -11.4

Combine like terms: 0 + -11.4 = -11.4
-7.2n + n2 = -11.4

The n term is -7.2n.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2n + 12.96 + n2 = -11.4 + 12.96

Reorder the terms:
12.96 + -7.2n + n2 = -11.4 + 12.96

Combine like terms: -11.4 + 12.96 = 1.56
12.96 + -7.2n + n2 = 1.56

Factor a perfect square on the left side:
(n + -3.6)(n + -3.6) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(n + -3.6) equal to 1.2489996 and -1.2489996.

Subproblem 1
n + -3.6 = 1.2489996

Simplifying
n + -3.6 = 1.2489996

Reorder the terms:
-3.6 + n = 1.2489996

Solving
-3.6 + n = 1.2489996

Solving for variable 'n'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + n = 1.2489996 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + n = 1.2489996 + 3.6
n = 1.2489996 + 3.6

Combine like terms: 1.2489996 + 3.6 = 4.8489996
n = 4.8489996

Simplifying
n = 4.8489996

Subproblem 2
n + -3.6 = -1.2489996

Simplifying
n + -3.6 = -1.2489996

Reorder the terms:
-3.6 + n = -1.2489996

Solving
-3.6 + n = -1.2489996

Solving for variable 'n'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + n = -1.2489996 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + n = -1.2489996 + 3.6
n = -1.2489996 + 3.6

Combine like terms: -1.2489996 + 3.6 = 2.3510004
n = 2.3510004

Simplifying
n = 2.3510004

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.8489996, 2.3510004}