m^2(m+11)+(m+11)=11

Solution for m^2(m+11)+(m+11)=11 equation:

Simplifying
m2(m + 11) + (m + 11) = 11

Reorder the terms:
m2(11 + m) + (m + 11) = 11
(11 * m2 + m * m2) + (m + 11) = 11
(11m2 + m3) + (m + 11) = 11

Reorder the terms:
11m2 + m3 + (11 + m) = 11

Remove parenthesis around (11 + m)
11m2 + m3 + 11 + m = 11

Reorder the terms:
11 + m + 11m2 + m3 = 11

Add '-11' to each side of the equation.
11 + m + 11m2 + -11 + m3 = 11 + -11

Reorder the terms:
11 + -11 + m + 11m2 + m3 = 11 + -11

Combine like terms: 11 + -11 = 0
0 + m + 11m2 + m3 = 11 + -11
m + 11m2 + m3 = 11 + -11

Combine like terms: 11 + -11 = 0
m + 11m2 + m3 = 0

Solving
m + 11m2 + m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm'.
m(1 + 11m + m2) = 0

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

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(1 + 11m + m2)' equal to zero and attempt to solve:

Simplifying
1 + 11m + m2 = 0

Solving
1 + 11m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 11m + -1 + m2 = 0 + -1

Reorder the terms:
1 + -1 + 11m + m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 11m + m2 = 0 + -1
11m + m2 = 0 + -1

Combine like terms: 0 + -1 = -1
11m + m2 = -1

The m term is 11m.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11m + 30.25 + m2 = -1 + 30.25

Reorder the terms:
30.25 + 11m + m2 = -1 + 30.25

Combine like terms: -1 + 30.25 = 29.25
30.25 + 11m + m2 = 29.25

Factor a perfect square on the left side:
(m + 5.5)(m + 5.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(m + 5.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
m + 5.5 = 5.408326913

Simplifying
m + 5.5 = 5.408326913

Reorder the terms:
5.5 + m = 5.408326913

Solving
5.5 + m = 5.408326913

Solving for variable 'm'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + m = 5.408326913 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + m = 5.408326913 + -5.5
m = 5.408326913 + -5.5

Combine like terms: 5.408326913 + -5.5 = -0.091673087
m = -0.091673087

Simplifying
m = -0.091673087

Subproblem 2
m + 5.5 = -5.408326913

Simplifying
m + 5.5 = -5.408326913

Reorder the terms:
5.5 + m = -5.408326913

Solving
5.5 + m = -5.408326913

Solving for variable 'm'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + m = -5.408326913 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + m = -5.408326913 + -5.5
m = -5.408326913 + -5.5

Combine like terms: -5.408326913 + -5.5 = -10.908326913
m = -10.908326913

Simplifying
m = -10.908326913

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.091673087, -10.908326913}
Solution
m = {0, -0.091673087, -10.908326913}