9(-3r-11)r=10

Solution for 9(-3r-11)r=10 equation:

Simplifying
9(-3r + -11) * r = 10

Reorder the terms:
9(-11 + -3r) * r = 10

Reorder the terms for easier multiplication:
9r(-11 + -3r) = 10
(-11 * 9r + -3r * 9r) = 10
(-99r + -27r2) = 10

Solving
-99r + -27r2 = 10

Solving for variable 'r'.

Reorder the terms:
-10 + -99r + -27r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -99r + -27r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 99r + 27r2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(10 + 99r + 27r2)' equal to zero and attempt to solve:

Simplifying
10 + 99r + 27r2 = 0

Solving
10 + 99r + 27r2 = 0

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

Divide each side by '27'.
0.3703703704 + 3.666666667r + r2 = 0

Move the constant term to the right:

Add '-0.3703703704' to each side of the equation.
0.3703703704 + 3.666666667r + -0.3703703704 + r2 = 0 + -0.3703703704

Reorder the terms:
0.3703703704 + -0.3703703704 + 3.666666667r + r2 = 0 + -0.3703703704

Combine like terms: 0.3703703704 + -0.3703703704 = 0.0000000000
0.0000000000 + 3.666666667r + r2 = 0 + -0.3703703704
3.666666667r + r2 = 0 + -0.3703703704

Combine like terms: 0 + -0.3703703704 = -0.3703703704
3.666666667r + r2 = -0.3703703704

The r term is 3.666666667r.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667r + 3.361111114 + r2 = -0.3703703704 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667r + r2 = -0.3703703704 + 3.361111114

Combine like terms: -0.3703703704 + 3.361111114 = 2.9907407436
3.361111114 + 3.666666667r + r2 = 2.9907407436

Factor a perfect square on the left side:
(r + 1.833333334)(r + 1.833333334) = 2.9907407436

Calculate the square root of the right side: 1.729375825

Break this problem into two subproblems by setting 
(r + 1.833333334) equal to 1.729375825 and -1.729375825.

Subproblem 1
r + 1.833333334 = 1.729375825

Simplifying
r + 1.833333334 = 1.729375825

Reorder the terms:
1.833333334 + r = 1.729375825

Solving
1.833333334 + r = 1.729375825

Solving for variable 'r'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + r = 1.729375825 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + r = 1.729375825 + -1.833333334
r = 1.729375825 + -1.833333334

Combine like terms: 1.729375825 + -1.833333334 = -0.103957509
r = -0.103957509

Simplifying
r = -0.103957509

Subproblem 2
r + 1.833333334 = -1.729375825

Simplifying
r + 1.833333334 = -1.729375825

Reorder the terms:
1.833333334 + r = -1.729375825

Solving
1.833333334 + r = -1.729375825

Solving for variable 'r'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + r = -1.729375825 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + r = -1.729375825 + -1.833333334
r = -1.729375825 + -1.833333334

Combine like terms: -1.729375825 + -1.833333334 = -3.562709159
r = -3.562709159

Simplifying
r = -3.562709159

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.103957509, -3.562709159}
Solution
r = {-0.103957509, -3.562709159}