10n^2-32n+21=0

Solution for 10n^2-32n+21=0 equation:

Simplifying
10n2 + -32n + 21 = 0

Reorder the terms:
21 + -32n + 10n2 = 0

Solving
21 + -32n + 10n2 = 0

Solving for variable 'n'.

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

Divide each side by '10'.
2.1 + -3.2n + n2 = 0

Move the constant term to the right:

Add '-2.1' to each side of the equation.
2.1 + -3.2n + -2.1 + n2 = 0 + -2.1

Reorder the terms:
2.1 + -2.1 + -3.2n + n2 = 0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + -3.2n + n2 = 0 + -2.1
-3.2n + n2 = 0 + -2.1

Combine like terms: 0 + -2.1 = -2.1
-3.2n + n2 = -2.1

The n term is -3.2n.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2n + 2.56 + n2 = -2.1 + 2.56

Reorder the terms:
2.56 + -3.2n + n2 = -2.1 + 2.56

Combine like terms: -2.1 + 2.56 = 0.46
2.56 + -3.2n + n2 = 0.46

Factor a perfect square on the left side:
(n + -1.6)(n + -1.6) = 0.46

Calculate the square root of the right side: 0.678232998

Break this problem into two subproblems by setting 
(n + -1.6) equal to 0.678232998 and -0.678232998.

Subproblem 1
n + -1.6 = 0.678232998

Simplifying
n + -1.6 = 0.678232998

Reorder the terms:
-1.6 + n = 0.678232998

Solving
-1.6 + n = 0.678232998

Solving for variable 'n'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + n = 0.678232998 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + n = 0.678232998 + 1.6
n = 0.678232998 + 1.6

Combine like terms: 0.678232998 + 1.6 = 2.278232998
n = 2.278232998

Simplifying
n = 2.278232998

Subproblem 2
n + -1.6 = -0.678232998

Simplifying
n + -1.6 = -0.678232998

Reorder the terms:
-1.6 + n = -0.678232998

Solving
-1.6 + n = -0.678232998

Solving for variable 'n'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + n = -0.678232998 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + n = -0.678232998 + 1.6
n = -0.678232998 + 1.6

Combine like terms: -0.678232998 + 1.6 = 0.921767002
n = 0.921767002

Simplifying
n = 0.921767002

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.278232998, 0.921767002}