(9r^3+5r^2+11r)+-(2r^3+9r-8r^2)=

Solution for (9r^3+5r^2+11r)+-(2r^3+9r-8r^2)= equation:

Simplifying
(9r3 + 5r2 + 11r) + -1(2r3 + 9r + -8r2) = 0

Reorder the terms:
(11r + 5r2 + 9r3) + -1(2r3 + 9r + -8r2) = 0

Remove parenthesis around (11r + 5r2 + 9r3)
11r + 5r2 + 9r3 + -1(2r3 + 9r + -8r2) = 0

Reorder the terms:
11r + 5r2 + 9r3 + -1(9r + -8r2 + 2r3) = 0
11r + 5r2 + 9r3 + (9r * -1 + -8r2 * -1 + 2r3 * -1) = 0
11r + 5r2 + 9r3 + (-9r + 8r2 + -2r3) = 0

Reorder the terms:
11r + -9r + 5r2 + 8r2 + 9r3 + -2r3 = 0

Combine like terms: 11r + -9r = 2r
2r + 5r2 + 8r2 + 9r3 + -2r3 = 0

Combine like terms: 5r2 + 8r2 = 13r2
2r + 13r2 + 9r3 + -2r3 = 0

Combine like terms: 9r3 + -2r3 = 7r3
2r + 13r2 + 7r3 = 0

Solving
2r + 13r2 + 7r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(2 + 13r + 7r2) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(2 + 13r + 7r2)' equal to zero and attempt to solve:

Simplifying
2 + 13r + 7r2 = 0

Solving
2 + 13r + 7r2 = 0

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

Divide each side by '7'.
0.2857142857 + 1.857142857r + r2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + 1.857142857r + -0.2857142857 + r2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + 1.857142857r + r2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + 1.857142857r + r2 = 0 + -0.2857142857
1.857142857r + r2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
1.857142857r + r2 = -0.2857142857

The r term is 1.857142857r.  Take half its coefficient (0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
1.857142857r + 0.8622448978 + r2 = -0.2857142857 + 0.8622448978

Reorder the terms:
0.8622448978 + 1.857142857r + r2 = -0.2857142857 + 0.8622448978

Combine like terms: -0.2857142857 + 0.8622448978 = 0.5765306121
0.8622448978 + 1.857142857r + r2 = 0.5765306121

Factor a perfect square on the left side:
(r + 0.9285714285)(r + 0.9285714285) = 0.5765306121

Calculate the square root of the right side: 0.759296129

Break this problem into two subproblems by setting 
(r + 0.9285714285) equal to 0.759296129 and -0.759296129.

Subproblem 1
r + 0.9285714285 = 0.759296129

Simplifying
r + 0.9285714285 = 0.759296129

Reorder the terms:
0.9285714285 + r = 0.759296129

Solving
0.9285714285 + r = 0.759296129

Solving for variable 'r'.

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

Add '-0.9285714285' to each side of the equation.
0.9285714285 + -0.9285714285 + r = 0.759296129 + -0.9285714285

Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000
0.0000000000 + r = 0.759296129 + -0.9285714285
r = 0.759296129 + -0.9285714285

Combine like terms: 0.759296129 + -0.9285714285 = -0.1692752995
r = -0.1692752995

Simplifying
r = -0.1692752995

Subproblem 2
r + 0.9285714285 = -0.759296129

Simplifying
r + 0.9285714285 = -0.759296129

Reorder the terms:
0.9285714285 + r = -0.759296129

Solving
0.9285714285 + r = -0.759296129

Solving for variable 'r'.

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

Add '-0.9285714285' to each side of the equation.
0.9285714285 + -0.9285714285 + r = -0.759296129 + -0.9285714285

Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000
0.0000000000 + r = -0.759296129 + -0.9285714285
r = -0.759296129 + -0.9285714285

Combine like terms: -0.759296129 + -0.9285714285 = -1.6878675575
r = -1.6878675575

Simplifying
r = -1.6878675575

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.1692752995, -1.6878675575}
Solution
r = {0, -0.1692752995, -1.6878675575}