4n^2-10n=-5

Solution for 4n^2-10n=-5 equation:

Simplifying
4n2 + -10n = -5

Reorder the terms:
-10n + 4n2 = -5

Solving
-10n + 4n2 = -5

Solving for variable 'n'.

Reorder the terms:
5 + -10n + 4n2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -10n + 4n2 = 0

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

Divide each side by '4'.
1.25 + -2.5n + n2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.5n + -1.25 + n2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.5n + n2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.5n + n2 = 0 + -1.25
-2.5n + n2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.5n + n2 = -1.25

The n term is -2.5n.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5n + 1.5625 + n2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + -2.5n + n2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + -2.5n + n2 = 0.3125

Factor a perfect square on the left side:
(n + -1.25)(n + -1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(n + -1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
n + -1.25 = 0.559016994

Simplifying
n + -1.25 = 0.559016994

Reorder the terms:
-1.25 + n = 0.559016994

Solving
-1.25 + n = 0.559016994

Solving for variable 'n'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + n = 0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + n = 0.559016994 + 1.25
n = 0.559016994 + 1.25

Combine like terms: 0.559016994 + 1.25 = 1.809016994
n = 1.809016994

Simplifying
n = 1.809016994

Subproblem 2
n + -1.25 = -0.559016994

Simplifying
n + -1.25 = -0.559016994

Reorder the terms:
-1.25 + n = -0.559016994

Solving
-1.25 + n = -0.559016994

Solving for variable 'n'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + n = -0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + n = -0.559016994 + 1.25
n = -0.559016994 + 1.25

Combine like terms: -0.559016994 + 1.25 = 0.690983006
n = 0.690983006

Simplifying
n = 0.690983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.809016994, 0.690983006}