-13=(5n-2)(n-5)

Solution for -13=(5n-2)(n-5) equation:

Simplifying
-13 = (5n + -2)(n + -5)

Reorder the terms:
-13 = (-2 + 5n)(n + -5)

Reorder the terms:
-13 = (-2 + 5n)(-5 + n)

Multiply (-2 + 5n) * (-5 + n)
-13 = (-2(-5 + n) + 5n * (-5 + n))
-13 = ((-5 * -2 + n * -2) + 5n * (-5 + n))
-13 = ((10 + -2n) + 5n * (-5 + n))
-13 = (10 + -2n + (-5 * 5n + n * 5n))
-13 = (10 + -2n + (-25n + 5n2))

Combine like terms: -2n + -25n = -27n
-13 = (10 + -27n + 5n2)

Solving
-13 = 10 + -27n + 5n2

Solving for variable 'n'.

Combine like terms: -13 + -10 = -23
-23 + 27n + -5n2 = 10 + -27n + 5n2 + -10 + 27n + -5n2

Reorder the terms:
-23 + 27n + -5n2 = 10 + -10 + -27n + 27n + 5n2 + -5n2

Combine like terms: 10 + -10 = 0
-23 + 27n + -5n2 = 0 + -27n + 27n + 5n2 + -5n2
-23 + 27n + -5n2 = -27n + 27n + 5n2 + -5n2

Combine like terms: -27n + 27n = 0
-23 + 27n + -5n2 = 0 + 5n2 + -5n2
-23 + 27n + -5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
-23 + 27n + -5n2 = 0

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

Divide each side by '-5'.
4.6 + -5.4n + n2 = 0

Move the constant term to the right:

Add '-4.6' to each side of the equation.
4.6 + -5.4n + -4.6 + n2 = 0 + -4.6

Reorder the terms:
4.6 + -4.6 + -5.4n + n2 = 0 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + -5.4n + n2 = 0 + -4.6
-5.4n + n2 = 0 + -4.6

Combine like terms: 0 + -4.6 = -4.6
-5.4n + n2 = -4.6

The n term is -5.4n.  Take half its coefficient (-2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
-5.4n + 7.29 + n2 = -4.6 + 7.29

Reorder the terms:
7.29 + -5.4n + n2 = -4.6 + 7.29

Combine like terms: -4.6 + 7.29 = 2.69
7.29 + -5.4n + n2 = 2.69

Factor a perfect square on the left side:
(n + -2.7)(n + -2.7) = 2.69

Calculate the square root of the right side: 1.640121947

Break this problem into two subproblems by setting 
(n + -2.7) equal to 1.640121947 and -1.640121947.

Subproblem 1
n + -2.7 = 1.640121947

Simplifying
n + -2.7 = 1.640121947

Reorder the terms:
-2.7 + n = 1.640121947

Solving
-2.7 + n = 1.640121947

Solving for variable 'n'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + n = 1.640121947 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + n = 1.640121947 + 2.7
n = 1.640121947 + 2.7

Combine like terms: 1.640121947 + 2.7 = 4.340121947
n = 4.340121947

Simplifying
n = 4.340121947

Subproblem 2
n + -2.7 = -1.640121947

Simplifying
n + -2.7 = -1.640121947

Reorder the terms:
-2.7 + n = -1.640121947

Solving
-2.7 + n = -1.640121947

Solving for variable 'n'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + n = -1.640121947 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + n = -1.640121947 + 2.7
n = -1.640121947 + 2.7

Combine like terms: -1.640121947 + 2.7 = 1.059878053
n = 1.059878053

Simplifying
n = 1.059878053

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.340121947, 1.059878053}