-9r(r+1)+6(1-3r)=

Solution for -9r(r+1)+6(1-3r)= equation:

Simplifying
-9r(r + 1) + 6(1 + -3r) = 0

Reorder the terms:
-9r(1 + r) + 6(1 + -3r) = 0
(1 * -9r + r * -9r) + 6(1 + -3r) = 0
(-9r + -9r2) + 6(1 + -3r) = 0
-9r + -9r2 + (1 * 6 + -3r * 6) = 0
-9r + -9r2 + (6 + -18r) = 0

Reorder the terms:
6 + -9r + -18r + -9r2 = 0

Combine like terms: -9r + -18r = -27r
6 + -27r + -9r2 = 0

Solving
6 + -27r + -9r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -9r + -3r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -9r + -3r2)' equal to zero and attempt to solve:

Simplifying
2 + -9r + -3r2 = 0

Solving
2 + -9r + -3r2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.6666666667 + 3r + r2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 3r + 0.6666666667 + r2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 3r + r2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 3r + r2 = 0 + 0.6666666667
3r + r2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
3r + r2 = 0.6666666667

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 0.6666666667 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 0.6666666667 + 2.25

Combine like terms: 0.6666666667 + 2.25 = 2.9166666667
2.25 + 3r + r2 = 2.9166666667

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 2.9166666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(r + 1.5) equal to 1.707825128 and -1.707825128.

Subproblem 1
r + 1.5 = 1.707825128

Simplifying
r + 1.5 = 1.707825128

Reorder the terms:
1.5 + r = 1.707825128

Solving
1.5 + r = 1.707825128

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 1.707825128 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 1.707825128 + -1.5
r = 1.707825128 + -1.5

Combine like terms: 1.707825128 + -1.5 = 0.207825128
r = 0.207825128

Simplifying
r = 0.207825128

Subproblem 2
r + 1.5 = -1.707825128

Simplifying
r + 1.5 = -1.707825128

Reorder the terms:
1.5 + r = -1.707825128

Solving
1.5 + r = -1.707825128

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -1.707825128 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -1.707825128 + -1.5
r = -1.707825128 + -1.5

Combine like terms: -1.707825128 + -1.5 = -3.207825128
r = -3.207825128

Simplifying
r = -3.207825128

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.207825128, -3.207825128}
Solution
r = {0.207825128, -3.207825128}