-8m-[3m(11+4m)+2]=9m

Solution for -8m-[3m(11+4m)+2]=9m equation:

Simplifying
-8m + -1[3m(11 + 4m) + 2] = 9m
-8m + -1[(11 * 3m + 4m * 3m) + 2] = 9m
-8m + -1[(33m + 12m2) + 2] = 9m

Reorder the terms:
-8m + -1[2 + 33m + 12m2] = 9m
-8m + [2 * -1 + 33m * -1 + 12m2 * -1] = 9m
-8m + [-2 + -33m + -12m2] = 9m

Reorder the terms:
-2 + -8m + -33m + -12m2 = 9m

Combine like terms: -8m + -33m = -41m
-2 + -41m + -12m2 = 9m

Solving
-2 + -41m + -12m2 = 9m

Solving for variable 'm'.

Reorder the terms:
-2 + -41m + -9m + -12m2 = 9m + -9m

Combine like terms: -41m + -9m = -50m
-2 + -50m + -12m2 = 9m + -9m

Combine like terms: 9m + -9m = 0
-2 + -50m + -12m2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 25m + 6m2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 25m + 6m2)' equal to zero and attempt to solve:

Simplifying
1 + 25m + 6m2 = 0

Solving
1 + 25m + 6m2 = 0

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

Divide each side by '6'.
0.1666666667 + 4.166666667m + m2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 4.166666667m + -0.1666666667 + m2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 4.166666667m + m2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 4.166666667m + m2 = 0 + -0.1666666667
4.166666667m + m2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
4.166666667m + m2 = -0.1666666667

The m term is 4.166666667m.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667m + 4.340277781 + m2 = -0.1666666667 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667m + m2 = -0.1666666667 + 4.340277781

Combine like terms: -0.1666666667 + 4.340277781 = 4.1736111143
4.340277781 + 4.166666667m + m2 = 4.1736111143

Factor a perfect square on the left side:
(m + 2.083333334)(m + 2.083333334) = 4.1736111143

Calculate the square root of the right side: 2.042941779

Break this problem into two subproblems by setting 
(m + 2.083333334) equal to 2.042941779 and -2.042941779.

Subproblem 1
m + 2.083333334 = 2.042941779

Simplifying
m + 2.083333334 = 2.042941779

Reorder the terms:
2.083333334 + m = 2.042941779

Solving
2.083333334 + m = 2.042941779

Solving for variable 'm'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + m = 2.042941779 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + m = 2.042941779 + -2.083333334
m = 2.042941779 + -2.083333334

Combine like terms: 2.042941779 + -2.083333334 = -0.040391555
m = -0.040391555

Simplifying
m = -0.040391555

Subproblem 2
m + 2.083333334 = -2.042941779

Simplifying
m + 2.083333334 = -2.042941779

Reorder the terms:
2.083333334 + m = -2.042941779

Solving
2.083333334 + m = -2.042941779

Solving for variable 'm'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + m = -2.042941779 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + m = -2.042941779 + -2.083333334
m = -2.042941779 + -2.083333334

Combine like terms: -2.042941779 + -2.083333334 = -4.126275113
m = -4.126275113

Simplifying
m = -4.126275113

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.040391555, -4.126275113}
Solution
m = {-0.040391555, -4.126275113}