10n^2-12n-9=0

Solution for 10n^2-12n-9=0 equation:

Simplifying
10n2 + -12n + -9 = 0

Reorder the terms:
-9 + -12n + 10n2 = 0

Solving
-9 + -12n + 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'.
-0.9 + -1.2n + n2 = 0

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + -1.2n + 0.9 + n2 = 0 + 0.9

Reorder the terms:
-0.9 + 0.9 + -1.2n + n2 = 0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + -1.2n + n2 = 0 + 0.9
-1.2n + n2 = 0 + 0.9

Combine like terms: 0 + 0.9 = 0.9
-1.2n + n2 = 0.9

The n term is -1.2n.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2n + 0.36 + n2 = 0.9 + 0.36

Reorder the terms:
0.36 + -1.2n + n2 = 0.9 + 0.36

Combine like terms: 0.9 + 0.36 = 1.26
0.36 + -1.2n + n2 = 1.26

Factor a perfect square on the left side:
(n + -0.6)(n + -0.6) = 1.26

Calculate the square root of the right side: 1.122497216

Break this problem into two subproblems by setting 
(n + -0.6) equal to 1.122497216 and -1.122497216.

Subproblem 1
n + -0.6 = 1.122497216

Simplifying
n + -0.6 = 1.122497216

Reorder the terms:
-0.6 + n = 1.122497216

Solving
-0.6 + n = 1.122497216

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = 1.122497216 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = 1.122497216 + 0.6
n = 1.122497216 + 0.6

Combine like terms: 1.122497216 + 0.6 = 1.722497216
n = 1.722497216

Simplifying
n = 1.722497216

Subproblem 2
n + -0.6 = -1.122497216

Simplifying
n + -0.6 = -1.122497216

Reorder the terms:
-0.6 + n = -1.122497216

Solving
-0.6 + n = -1.122497216

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = -1.122497216 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = -1.122497216 + 0.6
n = -1.122497216 + 0.6

Combine like terms: -1.122497216 + 0.6 = -0.522497216
n = -0.522497216

Simplifying
n = -0.522497216

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.722497216, -0.522497216}