6r^2-6r-6=0

Solution for 6r^2-6r-6=0 equation:

Simplifying
6r2 + -6r + -6 = 0

Reorder the terms:
-6 + -6r + 6r2 = 0

Solving
-6 + -6r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -1r + r2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1r + r2)' equal to zero and attempt to solve:

Simplifying
-1 + -1r + r2 = 0

Solving
-1 + -1r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + -1r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1r + r2 = 0 + 1
-1r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1r + r2 = 1

The r term is -1r.  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.
-1r + 0.25 + r2 = 1 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1r + r2 = 1.25

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

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(r + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
r + -0.5 = 1.118033989

Simplifying
r + -0.5 = 1.118033989

Reorder the terms:
-0.5 + r = 1.118033989

Solving
-0.5 + r = 1.118033989

Solving for variable 'r'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + r = 1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r = 1.118033989 + 0.5
r = 1.118033989 + 0.5

Combine like terms: 1.118033989 + 0.5 = 1.618033989
r = 1.618033989

Simplifying
r = 1.618033989

Subproblem 2
r + -0.5 = -1.118033989

Simplifying
r + -0.5 = -1.118033989

Reorder the terms:
-0.5 + r = -1.118033989

Solving
-0.5 + r = -1.118033989

Solving for variable 'r'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + r = -1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r = -1.118033989 + 0.5
r = -1.118033989 + 0.5

Combine like terms: -1.118033989 + 0.5 = -0.618033989
r = -0.618033989

Simplifying
r = -0.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.618033989, -0.618033989}
Solution
r = {1.618033989, -0.618033989}