26=n(n+4)

Solution for 26=n(n+4) equation:

Simplifying
26 = n(n + 4)

Reorder the terms:
26 = n(4 + n)
26 = (4 * n + n * n)
26 = (4n + n2)

Solving
26 = 4n + n2

Solving for variable 'n'.

Reorder the terms:
26 + -4n + -1n2 = 4n + -4n + n2 + -1n2

Combine like terms: 4n + -4n = 0
26 + -4n + -1n2 = 0 + n2 + -1n2
26 + -4n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
26 + -4n + -1n2 = 0

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

Divide each side by '-1'.
-26 + 4n + n2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 4n + 26 + n2 = 0 + 26

Reorder the terms:
-26 + 26 + 4n + n2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 4n + n2 = 0 + 26
4n + n2 = 0 + 26

Combine like terms: 0 + 26 = 26
4n + n2 = 26

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 26 + 4

Reorder the terms:
4 + 4n + n2 = 26 + 4

Combine like terms: 26 + 4 = 30
4 + 4n + n2 = 30

Factor a perfect square on the left side:
(n + 2)(n + 2) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(n + 2) equal to 5.477225575 and -5.477225575.

Subproblem 1
n + 2 = 5.477225575

Simplifying
n + 2 = 5.477225575

Reorder the terms:
2 + n = 5.477225575

Solving
2 + n = 5.477225575

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = 5.477225575 + -2

Combine like terms: 2 + -2 = 0
0 + n = 5.477225575 + -2
n = 5.477225575 + -2

Combine like terms: 5.477225575 + -2 = 3.477225575
n = 3.477225575

Simplifying
n = 3.477225575

Subproblem 2
n + 2 = -5.477225575

Simplifying
n + 2 = -5.477225575

Reorder the terms:
2 + n = -5.477225575

Solving
2 + n = -5.477225575

Solving for variable 'n'.

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

Add '-2' to each side of the equation.
2 + -2 + n = -5.477225575 + -2

Combine like terms: 2 + -2 = 0
0 + n = -5.477225575 + -2
n = -5.477225575 + -2

Combine like terms: -5.477225575 + -2 = -7.477225575
n = -7.477225575

Simplifying
n = -7.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.477225575, -7.477225575}