6n^2+71=-12n

Solution for 6n^2+71=-12n equation:

Simplifying
6n2 + 71 = -12n

Reorder the terms:
71 + 6n2 = -12n

Solving
71 + 6n2 = -12n

Solving for variable 'n'.

Reorder the terms:
71 + 12n + 6n2 = -12n + 12n

Combine like terms: -12n + 12n = 0
71 + 12n + 6n2 = 0

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

Divide each side by '6'.
11.83333333 + 2n + n2 = 0

Move the constant term to the right:

Add '-11.83333333' to each side of the equation.
11.83333333 + 2n + -11.83333333 + n2 = 0 + -11.83333333

Reorder the terms:
11.83333333 + -11.83333333 + 2n + n2 = 0 + -11.83333333

Combine like terms: 11.83333333 + -11.83333333 = 0.00000000
0.00000000 + 2n + n2 = 0 + -11.83333333
2n + n2 = 0 + -11.83333333

Combine like terms: 0 + -11.83333333 = -11.83333333
2n + n2 = -11.83333333

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 = -11.83333333 + 1

Reorder the terms:
1 + 2n + n2 = -11.83333333 + 1

Combine like terms: -11.83333333 + 1 = -10.83333333
1 + 2n + n2 = -10.83333333

Factor a perfect square on the left side:
(n + 1)(n + 1) = -10.83333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.