3+5n(n-2)=62

Solution for 3+5n(n-2)=62 equation:

Simplifying
3 + 5n(n + -2) = 62

Reorder the terms:
3 + 5n(-2 + n) = 62
3 + (-2 * 5n + n * 5n) = 62
3 + (-10n + 5n2) = 62

Solving
3 + -10n + 5n2 = 62

Solving for variable 'n'.

Reorder the terms:
3 + -62 + -10n + 5n2 = 62 + -62

Combine like terms: 3 + -62 = -59
-59 + -10n + 5n2 = 62 + -62

Combine like terms: 62 + -62 = 0
-59 + -10n + 5n2 = 0

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

Divide each side by '5'.
-11.8 + -2n + n2 = 0

Move the constant term to the right:

Add '11.8' to each side of the equation.
-11.8 + -2n + 11.8 + n2 = 0 + 11.8

Reorder the terms:
-11.8 + 11.8 + -2n + n2 = 0 + 11.8

Combine like terms: -11.8 + 11.8 = 0.0
0.0 + -2n + n2 = 0 + 11.8
-2n + n2 = 0 + 11.8

Combine like terms: 0 + 11.8 = 11.8
-2n + n2 = 11.8

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 = 11.8 + 1

Reorder the terms:
1 + -2n + n2 = 11.8 + 1

Combine like terms: 11.8 + 1 = 12.8
1 + -2n + n2 = 12.8

Factor a perfect square on the left side:
(n + -1)(n + -1) = 12.8

Calculate the square root of the right side: 3.577708764

Break this problem into two subproblems by setting 
(n + -1) equal to 3.577708764 and -3.577708764.

Subproblem 1
n + -1 = 3.577708764

Simplifying
n + -1 = 3.577708764

Reorder the terms:
-1 + n = 3.577708764

Solving
-1 + n = 3.577708764

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 = 3.577708764 + 1

Combine like terms: -1 + 1 = 0
0 + n = 3.577708764 + 1
n = 3.577708764 + 1

Combine like terms: 3.577708764 + 1 = 4.577708764
n = 4.577708764

Simplifying
n = 4.577708764

Subproblem 2
n + -1 = -3.577708764

Simplifying
n + -1 = -3.577708764

Reorder the terms:
-1 + n = -3.577708764

Solving
-1 + n = -3.577708764

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 = -3.577708764 + 1

Combine like terms: -1 + 1 = 0
0 + n = -3.577708764 + 1
n = -3.577708764 + 1

Combine like terms: -3.577708764 + 1 = -2.577708764
n = -2.577708764

Simplifying
n = -2.577708764

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.577708764, -2.577708764}