5n(n+2)=4-3

Solution for 5n(n+2)=4-3 equation:

Simplifying
5n(n + 2) = 4 + -3

Reorder the terms:
5n(2 + n) = 4 + -3
(2 * 5n + n * 5n) = 4 + -3
(10n + 5n2) = 4 + -3

Combine like terms: 4 + -3 = 1
10n + 5n2 = 1

Solving
10n + 5n2 = 1

Solving for variable 'n'.

Reorder the terms:
-1 + 10n + 5n2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 10n + 5n2 = 0

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

Divide each side by '5'.
-0.2 + 2n + n2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 2n + 0.2 + n2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 2n + n2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 2n + n2 = 0 + 0.2
2n + n2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
2n + n2 = 0.2

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 0.2 + 1

Reorder the terms:
1 + 2n + n2 = 0.2 + 1

Combine like terms: 0.2 + 1 = 1.2
1 + 2n + n2 = 1.2

Factor a perfect square on the left side:
(n + 1)(n + 1) = 1.2

Calculate the square root of the right side: 1.095445115

Break this problem into two subproblems by setting 
(n + 1) equal to 1.095445115 and -1.095445115.

Subproblem 1
n + 1 = 1.095445115

Simplifying
n + 1 = 1.095445115

Reorder the terms:
1 + n = 1.095445115

Solving
1 + n = 1.095445115

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 1.095445115 + -1

Combine like terms: 1 + -1 = 0
0 + n = 1.095445115 + -1
n = 1.095445115 + -1

Combine like terms: 1.095445115 + -1 = 0.095445115
n = 0.095445115

Simplifying
n = 0.095445115

Subproblem 2
n + 1 = -1.095445115

Simplifying
n + 1 = -1.095445115

Reorder the terms:
1 + n = -1.095445115

Solving
1 + n = -1.095445115

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -1.095445115 + -1

Combine like terms: 1 + -1 = 0
0 + n = -1.095445115 + -1
n = -1.095445115 + -1

Combine like terms: -1.095445115 + -1 = -2.095445115
n = -2.095445115

Simplifying
n = -2.095445115

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.095445115, -2.095445115}