5n(n+2)-8=2n

Solution for 5n(n+2)-8=2n equation:

Simplifying
5n(n + 2) + -8 = 2n

Reorder the terms:
5n(2 + n) + -8 = 2n
(2 * 5n + n * 5n) + -8 = 2n
(10n + 5n2) + -8 = 2n

Reorder the terms:
-8 + 10n + 5n2 = 2n

Solving
-8 + 10n + 5n2 = 2n

Solving for variable 'n'.

Reorder the terms:
-8 + 10n + -2n + 5n2 = 2n + -2n

Combine like terms: 10n + -2n = 8n
-8 + 8n + 5n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-8 + 8n + 5n2 = 0

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

Divide each side by '5'.
-1.6 + 1.6n + n2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 1.6n + 1.6 + n2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 1.6n + n2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 1.6n + n2 = 0 + 1.6
1.6n + n2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
1.6n + n2 = 1.6

The n term is 1.6n.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6n + 0.64 + n2 = 1.6 + 0.64

Reorder the terms:
0.64 + 1.6n + n2 = 1.6 + 0.64

Combine like terms: 1.6 + 0.64 = 2.24
0.64 + 1.6n + n2 = 2.24

Factor a perfect square on the left side:
(n + 0.8)(n + 0.8) = 2.24

Calculate the square root of the right side: 1.496662955

Break this problem into two subproblems by setting 
(n + 0.8) equal to 1.496662955 and -1.496662955.

Subproblem 1
n + 0.8 = 1.496662955

Simplifying
n + 0.8 = 1.496662955

Reorder the terms:
0.8 + n = 1.496662955

Solving
0.8 + n = 1.496662955

Solving for variable 'n'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + n = 1.496662955 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + n = 1.496662955 + -0.8
n = 1.496662955 + -0.8

Combine like terms: 1.496662955 + -0.8 = 0.696662955
n = 0.696662955

Simplifying
n = 0.696662955

Subproblem 2
n + 0.8 = -1.496662955

Simplifying
n + 0.8 = -1.496662955

Reorder the terms:
0.8 + n = -1.496662955

Solving
0.8 + n = -1.496662955

Solving for variable 'n'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + n = -1.496662955 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + n = -1.496662955 + -0.8
n = -1.496662955 + -0.8

Combine like terms: -1.496662955 + -0.8 = -2.296662955
n = -2.296662955

Simplifying
n = -2.296662955

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.696662955, -2.296662955}