4n^2+6=-n

Solution for 4n^2+6=-n equation:

Simplifying
4n2 + 6 = -1n

Reorder the terms:
6 + 4n2 = -1n

Solving
6 + 4n2 = -1n

Solving for variable 'n'.

Reorder the terms:
6 + n + 4n2 = -1n + n

Combine like terms: -1n + n = 0
6 + n + 4n2 = 0

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

Divide each side by '4'.
1.5 + 0.25n + n2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.25n + -1.5 + n2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.25n + n2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.25n + n2 = 0 + -1.5
0.25n + n2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.25n + n2 = -1.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25n + 0.25 + n2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.25n + n2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.25n + n2 = -1.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.