12+9=3+12n+5n^2

Solution for 12+9=3+12n+5n^2 equation:

Simplifying
12 + 9 = 3 + 12n + 5n2

Combine like terms: 12 + 9 = 21
21 = 3 + 12n + 5n2

Solving
21 = 3 + 12n + 5n2

Solving for variable 'n'.

Combine like terms: 21 + -3 = 18
18 + -12n + -5n2 = 3 + 12n + 5n2 + -3 + -12n + -5n2

Reorder the terms:
18 + -12n + -5n2 = 3 + -3 + 12n + -12n + 5n2 + -5n2

Combine like terms: 3 + -3 = 0
18 + -12n + -5n2 = 0 + 12n + -12n + 5n2 + -5n2
18 + -12n + -5n2 = 12n + -12n + 5n2 + -5n2

Combine like terms: 12n + -12n = 0
18 + -12n + -5n2 = 0 + 5n2 + -5n2
18 + -12n + -5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
18 + -12n + -5n2 = 0

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

Divide each side by '-5'.
-3.6 + 2.4n + n2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 2.4n + 3.6 + n2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 2.4n + n2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 2.4n + n2 = 0 + 3.6
2.4n + n2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
2.4n + n2 = 3.6

The n term is 2.4n.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4n + 1.44 + n2 = 3.6 + 1.44

Reorder the terms:
1.44 + 2.4n + n2 = 3.6 + 1.44

Combine like terms: 3.6 + 1.44 = 5.04
1.44 + 2.4n + n2 = 5.04

Factor a perfect square on the left side:
(n + 1.2)(n + 1.2) = 5.04

Calculate the square root of the right side: 2.244994432

Break this problem into two subproblems by setting 
(n + 1.2) equal to 2.244994432 and -2.244994432.

Subproblem 1
n + 1.2 = 2.244994432

Simplifying
n + 1.2 = 2.244994432

Reorder the terms:
1.2 + n = 2.244994432

Solving
1.2 + n = 2.244994432

Solving for variable 'n'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + n = 2.244994432 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + n = 2.244994432 + -1.2
n = 2.244994432 + -1.2

Combine like terms: 2.244994432 + -1.2 = 1.044994432
n = 1.044994432

Simplifying
n = 1.044994432

Subproblem 2
n + 1.2 = -2.244994432

Simplifying
n + 1.2 = -2.244994432

Reorder the terms:
1.2 + n = -2.244994432

Solving
1.2 + n = -2.244994432

Solving for variable 'n'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + n = -2.244994432 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + n = -2.244994432 + -1.2
n = -2.244994432 + -1.2

Combine like terms: -2.244994432 + -1.2 = -3.444994432
n = -3.444994432

Simplifying
n = -3.444994432

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.044994432, -3.444994432}