n*12-(-35)=n^2

Solution for n*12-(-35)=n^2 equation:

Simplifying
n * 12 + -1(-35) = n2

Reorder the terms for easier multiplication:
12n + -1(-35) = n2

Multiply -1 * -35
12n + 35 = n2

Reorder the terms:
35 + 12n = n2

Solving
35 + 12n = n2

Solving for variable 'n'.

Combine like terms: n2 + -1n2 = 0
35 + 12n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-35 + -12n + n2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -12n + 35 + n2 = 0 + 35

Reorder the terms:
-35 + 35 + -12n + n2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -12n + n2 = 0 + 35
-12n + n2 = 0 + 35

Combine like terms: 0 + 35 = 35
-12n + n2 = 35

The n term is -12n.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12n + 36 + n2 = 35 + 36

Reorder the terms:
36 + -12n + n2 = 35 + 36

Combine like terms: 35 + 36 = 71
36 + -12n + n2 = 71

Factor a perfect square on the left side:
(n + -6)(n + -6) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(n + -6) equal to 8.426149773 and -8.426149773.

Subproblem 1
n + -6 = 8.426149773

Simplifying
n + -6 = 8.426149773

Reorder the terms:
-6 + n = 8.426149773

Solving
-6 + n = 8.426149773

Solving for variable 'n'.

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

Add '6' to each side of the equation.
-6 + 6 + n = 8.426149773 + 6

Combine like terms: -6 + 6 = 0
0 + n = 8.426149773 + 6
n = 8.426149773 + 6

Combine like terms: 8.426149773 + 6 = 14.426149773
n = 14.426149773

Simplifying
n = 14.426149773

Subproblem 2
n + -6 = -8.426149773

Simplifying
n + -6 = -8.426149773

Reorder the terms:
-6 + n = -8.426149773

Solving
-6 + n = -8.426149773

Solving for variable 'n'.

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

Add '6' to each side of the equation.
-6 + 6 + n = -8.426149773 + 6

Combine like terms: -6 + 6 = 0
0 + n = -8.426149773 + 6
n = -8.426149773 + 6

Combine like terms: -8.426149773 + 6 = -2.426149773
n = -2.426149773

Simplifying
n = -2.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {14.426149773, -2.426149773}