2n(n-5)=4(n+2)

Solution for 2n(n-5)=4(n+2) equation:

Simplifying
2n(n + -5) = 4(n + 2)

Reorder the terms:
2n(-5 + n) = 4(n + 2)
(-5 * 2n + n * 2n) = 4(n + 2)
(-10n + 2n2) = 4(n + 2)

Reorder the terms:
-10n + 2n2 = 4(2 + n)
-10n + 2n2 = (2 * 4 + n * 4)
-10n + 2n2 = (8 + 4n)

Solving
-10n + 2n2 = 8 + 4n

Solving for variable 'n'.

Reorder the terms:
-8 + -10n + -4n + 2n2 = 8 + 4n + -8 + -4n

Combine like terms: -10n + -4n = -14n
-8 + -14n + 2n2 = 8 + 4n + -8 + -4n

Reorder the terms:
-8 + -14n + 2n2 = 8 + -8 + 4n + -4n

Combine like terms: 8 + -8 = 0
-8 + -14n + 2n2 = 0 + 4n + -4n
-8 + -14n + 2n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
-8 + -14n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -7n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -7n + n2)' equal to zero and attempt to solve:

Simplifying
-4 + -7n + n2 = 0

Solving
-4 + -7n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -7n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + -7n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7n + n2 = 0 + 4
-7n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
-7n + n2 = 4

The n term is -7n.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7n + 12.25 + n2 = 4 + 12.25

Reorder the terms:
12.25 + -7n + n2 = 4 + 12.25

Combine like terms: 4 + 12.25 = 16.25
12.25 + -7n + n2 = 16.25

Factor a perfect square on the left side:
(n + -3.5)(n + -3.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(n + -3.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
n + -3.5 = 4.031128874

Simplifying
n + -3.5 = 4.031128874

Reorder the terms:
-3.5 + n = 4.031128874

Solving
-3.5 + n = 4.031128874

Solving for variable 'n'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + n = 4.031128874 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + n = 4.031128874 + 3.5
n = 4.031128874 + 3.5

Combine like terms: 4.031128874 + 3.5 = 7.531128874
n = 7.531128874

Simplifying
n = 7.531128874

Subproblem 2
n + -3.5 = -4.031128874

Simplifying
n + -3.5 = -4.031128874

Reorder the terms:
-3.5 + n = -4.031128874

Solving
-3.5 + n = -4.031128874

Solving for variable 'n'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + n = -4.031128874 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + n = -4.031128874 + 3.5
n = -4.031128874 + 3.5

Combine like terms: -4.031128874 + 3.5 = -0.531128874
n = -0.531128874

Simplifying
n = -0.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.531128874, -0.531128874}
Solution
n = {7.531128874, -0.531128874}