4n^2=-2n-1

Solution for 4n^2=-2n-1 equation:

Simplifying
4n2 = -2n + -1

Reorder the terms:
4n2 = -1 + -2n

Solving
4n2 = -1 + -2n

Solving for variable 'n'.

Reorder the terms:
1 + 2n + 4n2 = -1 + -2n + 1 + 2n

Reorder the terms:
1 + 2n + 4n2 = -1 + 1 + -2n + 2n

Combine like terms: -1 + 1 = 0
1 + 2n + 4n2 = 0 + -2n + 2n
1 + 2n + 4n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
1 + 2n + 4n2 = 0

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

Divide each side by '4'.
0.25 + 0.5n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 0.5n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 0.5n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 0.5n + n2 = 0 + -0.25
0.5n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
0.5n + n2 = -0.25

The n term is 0.5n.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5n + 0.0625 + n2 = -0.25 + 0.0625

Reorder the terms:
0.0625 + 0.5n + n2 = -0.25 + 0.0625

Combine like terms: -0.25 + 0.0625 = -0.1875
0.0625 + 0.5n + n2 = -0.1875

Factor a perfect square on the left side:
(n + 0.25)(n + 0.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.