3n^2+6n-73=0

Solution for 3n^2+6n-73=0 equation:

Simplifying
3n2 + 6n + -73 = 0

Reorder the terms:
-73 + 6n + 3n2 = 0

Solving
-73 + 6n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-24.33333333 + 2n + n2 = 0

Move the constant term to the right:

Add '24.33333333' to each side of the equation.
-24.33333333 + 2n + 24.33333333 + n2 = 0 + 24.33333333

Reorder the terms:
-24.33333333 + 24.33333333 + 2n + n2 = 0 + 24.33333333

Combine like terms: -24.33333333 + 24.33333333 = 0.00000000
0.00000000 + 2n + n2 = 0 + 24.33333333
2n + n2 = 0 + 24.33333333

Combine like terms: 0 + 24.33333333 = 24.33333333
2n + n2 = 24.33333333

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 24.33333333 + 1

Reorder the terms:
1 + 2n + n2 = 24.33333333 + 1

Combine like terms: 24.33333333 + 1 = 25.33333333
1 + 2n + n2 = 25.33333333

Factor a perfect square on the left side:
(n + 1)(n + 1) = 25.33333333

Calculate the square root of the right side: 5.033222957

Break this problem into two subproblems by setting 
(n + 1) equal to 5.033222957 and -5.033222957.

Subproblem 1
n + 1 = 5.033222957

Simplifying
n + 1 = 5.033222957

Reorder the terms:
1 + n = 5.033222957

Solving
1 + n = 5.033222957

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 5.033222957 + -1

Combine like terms: 1 + -1 = 0
0 + n = 5.033222957 + -1
n = 5.033222957 + -1

Combine like terms: 5.033222957 + -1 = 4.033222957
n = 4.033222957

Simplifying
n = 4.033222957

Subproblem 2
n + 1 = -5.033222957

Simplifying
n + 1 = -5.033222957

Reorder the terms:
1 + n = -5.033222957

Solving
1 + n = -5.033222957

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -5.033222957 + -1

Combine like terms: 1 + -1 = 0
0 + n = -5.033222957 + -1
n = -5.033222957 + -1

Combine like terms: -5.033222957 + -1 = -6.033222957
n = -6.033222957

Simplifying
n = -6.033222957

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.033222957, -6.033222957}