-4n^2+2n-2=-3

Solution for -4n^2+2n-2=-3 equation:

Simplifying
-4n2 + 2n + -2 = -3

Reorder the terms:
-2 + 2n + -4n2 = -3

Solving
-2 + 2n + -4n2 = -3

Solving for variable 'n'.

Reorder the terms:
-2 + 3 + 2n + -4n2 = -3 + 3

Combine like terms: -2 + 3 = 1
1 + 2n + -4n2 = -3 + 3

Combine like terms: -3 + 3 = 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 = 0.3125
0.0625 + -0.5n + n2 = 0.3125

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(n + -0.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
n + -0.25 = 0.559016994

Simplifying
n + -0.25 = 0.559016994

Reorder the terms:
-0.25 + n = 0.559016994

Solving
-0.25 + n = 0.559016994

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = 0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = 0.559016994 + 0.25
n = 0.559016994 + 0.25

Combine like terms: 0.559016994 + 0.25 = 0.809016994
n = 0.809016994

Simplifying
n = 0.809016994

Subproblem 2
n + -0.25 = -0.559016994

Simplifying
n + -0.25 = -0.559016994

Reorder the terms:
-0.25 + n = -0.559016994

Solving
-0.25 + n = -0.559016994

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = -0.559016994 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = -0.559016994 + 0.25
n = -0.559016994 + 0.25

Combine like terms: -0.559016994 + 0.25 = -0.309016994
n = -0.309016994

Simplifying
n = -0.309016994

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.809016994, -0.309016994}