-4r^2-4r=6

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

Simplifying
-4r2 + -4r = 6

Reorder the terms:
-4r + -4r2 = 6

Solving
-4r + -4r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + -4r + -4r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -4r + -4r2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 2r + 2r2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 2r + 2r2)' equal to zero and attempt to solve:

Simplifying
3 + 2r + 2r2 = 0

Solving
3 + 2r + 2r2 = 0

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

Divide each side by '2'.
1.5 + r + r2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + r + -1.5 + r2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + r + r2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r + r2 = 0 + -1.5
r + r2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
r + r2 = -1.5

The r term is r.  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.
 + 0.25 + r2 = -1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
1.25 + r2 = -1.25

Factor a perfect square on the left side:
(r + 0.5)(r + 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.