6r^2-12r-9=-4

Solution for 6r^2-12r-9=-4 equation:

Simplifying
6r2 + -12r + -9 = -4

Reorder the terms:
-9 + -12r + 6r2 = -4

Solving
-9 + -12r + 6r2 = -4

Solving for variable 'r'.

Reorder the terms:
-9 + 4 + -12r + 6r2 = -4 + 4

Combine like terms: -9 + 4 = -5
-5 + -12r + 6r2 = -4 + 4

Combine like terms: -4 + 4 = 0
-5 + -12r + 6r2 = 0

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

Divide each side by '6'.
-0.8333333333 + -2r + r2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -2r + 0.8333333333 + r2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -2r + r2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -2r + r2 = 0 + 0.8333333333
-2r + r2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-2r + r2 = 0.8333333333

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 0.8333333333 + 1

Reorder the terms:
1 + -2r + r2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + -2r + r2 = 1.8333333333

Factor a perfect square on the left side:
(r + -1)(r + -1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(r + -1) equal to 1.354006401 and -1.354006401.

Subproblem 1
r + -1 = 1.354006401

Simplifying
r + -1 = 1.354006401

Reorder the terms:
-1 + r = 1.354006401

Solving
-1 + r = 1.354006401

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 1.354006401 + 1

Combine like terms: -1 + 1 = 0
0 + r = 1.354006401 + 1
r = 1.354006401 + 1

Combine like terms: 1.354006401 + 1 = 2.354006401
r = 2.354006401

Simplifying
r = 2.354006401

Subproblem 2
r + -1 = -1.354006401

Simplifying
r + -1 = -1.354006401

Reorder the terms:
-1 + r = -1.354006401

Solving
-1 + r = -1.354006401

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -1.354006401 + 1

Combine like terms: -1 + 1 = 0
0 + r = -1.354006401 + 1
r = -1.354006401 + 1

Combine like terms: -1.354006401 + 1 = -0.354006401
r = -0.354006401

Simplifying
r = -0.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.354006401, -0.354006401}