-44m(m+3)=24

Solution for -44m(m+3)=24 equation:

Simplifying
-44m(m + 3) = 24

Reorder the terms:
-44m(3 + m) = 24
(3 * -44m + m * -44m) = 24
(-132m + -44m2) = 24

Solving
-132m + -44m2 = 24

Solving for variable 'm'.

Reorder the terms:
-24 + -132m + -44m2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -132m + -44m2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(6 + 33m + 11m2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(6 + 33m + 11m2)' equal to zero and attempt to solve:

Simplifying
6 + 33m + 11m2 = 0

Solving
6 + 33m + 11m2 = 0

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

Divide each side by '11'.
0.5454545455 + 3m + m2 = 0

Move the constant term to the right:

Add '-0.5454545455' to each side of the equation.
0.5454545455 + 3m + -0.5454545455 + m2 = 0 + -0.5454545455

Reorder the terms:
0.5454545455 + -0.5454545455 + 3m + m2 = 0 + -0.5454545455

Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000
0.0000000000 + 3m + m2 = 0 + -0.5454545455
3m + m2 = 0 + -0.5454545455

Combine like terms: 0 + -0.5454545455 = -0.5454545455
3m + m2 = -0.5454545455

The m term is 3m.  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.
3m + 2.25 + m2 = -0.5454545455 + 2.25

Reorder the terms:
2.25 + 3m + m2 = -0.5454545455 + 2.25

Combine like terms: -0.5454545455 + 2.25 = 1.7045454545
2.25 + 3m + m2 = 1.7045454545

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 1.7045454545

Calculate the square root of the right side: 1.30558242

Break this problem into two subproblems by setting 
(m + 1.5) equal to 1.30558242 and -1.30558242.

Subproblem 1
m + 1.5 = 1.30558242

Simplifying
m + 1.5 = 1.30558242

Reorder the terms:
1.5 + m = 1.30558242

Solving
1.5 + m = 1.30558242

Solving for variable 'm'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = 1.30558242 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = 1.30558242 + -1.5
m = 1.30558242 + -1.5

Combine like terms: 1.30558242 + -1.5 = -0.19441758
m = -0.19441758

Simplifying
m = -0.19441758

Subproblem 2
m + 1.5 = -1.30558242

Simplifying
m + 1.5 = -1.30558242

Reorder the terms:
1.5 + m = -1.30558242

Solving
1.5 + m = -1.30558242

Solving for variable 'm'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = -1.30558242 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = -1.30558242 + -1.5
m = -1.30558242 + -1.5

Combine like terms: -1.30558242 + -1.5 = -2.80558242
m = -2.80558242

Simplifying
m = -2.80558242

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.19441758, -2.80558242}
Solution
m = {-0.19441758, -2.80558242}