-4x^2-x=6

Solution for -4x^2-x=6 equation:

Simplifying
-4x2 + -1x = 6

Reorder the terms:
-1x + -4x2 = 6

Solving
-1x + -4x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -1x + -4x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -1x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
6 + x + 4x2 = 0

Solving
6 + x + 4x2 = 0

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

Divide each side by '4'.
1.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.25x + x2 = 0 + -1.5
0.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.25x + x2 = -1.5

The x term is x.  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.
0.25x + 0.25 + x2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.25x + x2 = -1.25

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.