10n^2=3n+6

Solution for 10n^2=3n+6 equation:

Simplifying
10n2 = 3n + 6

Reorder the terms:
10n2 = 6 + 3n

Solving
10n2 = 6 + 3n

Solving for variable 'n'.

Reorder the terms:
-6 + -3n + 10n2 = 6 + 3n + -6 + -3n

Reorder the terms:
-6 + -3n + 10n2 = 6 + -6 + 3n + -3n

Combine like terms: 6 + -6 = 0
-6 + -3n + 10n2 = 0 + 3n + -3n
-6 + -3n + 10n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-6 + -3n + 10n2 = 0

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

Divide each side by '10'.
-0.6 + -0.3n + n2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.3n + 0.6 + n2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.3n + n2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.3n + n2 = 0 + 0.6
-0.3n + n2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.3n + n2 = 0.6

The n term is -0.3n.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3n + 0.0225 + n2 = 0.6 + 0.0225

Reorder the terms:
0.0225 + -0.3n + n2 = 0.6 + 0.0225

Combine like terms: 0.6 + 0.0225 = 0.6225
0.0225 + -0.3n + n2 = 0.6225

Factor a perfect square on the left side:
(n + -0.15)(n + -0.15) = 0.6225

Calculate the square root of the right side: 0.788986692

Break this problem into two subproblems by setting 
(n + -0.15) equal to 0.788986692 and -0.788986692.

Subproblem 1
n + -0.15 = 0.788986692

Simplifying
n + -0.15 = 0.788986692

Reorder the terms:
-0.15 + n = 0.788986692

Solving
-0.15 + n = 0.788986692

Solving for variable 'n'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + n = 0.788986692 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + n = 0.788986692 + 0.15
n = 0.788986692 + 0.15

Combine like terms: 0.788986692 + 0.15 = 0.938986692
n = 0.938986692

Simplifying
n = 0.938986692

Subproblem 2
n + -0.15 = -0.788986692

Simplifying
n + -0.15 = -0.788986692

Reorder the terms:
-0.15 + n = -0.788986692

Solving
-0.15 + n = -0.788986692

Solving for variable 'n'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + n = -0.788986692 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + n = -0.788986692 + 0.15
n = -0.788986692 + 0.15

Combine like terms: -0.788986692 + 0.15 = -0.638986692
n = -0.638986692

Simplifying
n = -0.638986692

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.938986692, -0.638986692}