-24m(m+3)=4+2m

Solution for -24m(m+3)=4+2m equation:

Simplifying
-24m(m + 3) = 4 + 2m

Reorder the terms:
-24m(3 + m) = 4 + 2m
(3 * -24m + m * -24m) = 4 + 2m
(-72m + -24m2) = 4 + 2m

Solving
-72m + -24m2 = 4 + 2m

Solving for variable 'm'.

Reorder the terms:
-4 + -72m + -2m + -24m2 = 4 + 2m + -4 + -2m

Combine like terms: -72m + -2m = -74m
-4 + -74m + -24m2 = 4 + 2m + -4 + -2m

Reorder the terms:
-4 + -74m + -24m2 = 4 + -4 + 2m + -2m

Combine like terms: 4 + -4 = 0
-4 + -74m + -24m2 = 0 + 2m + -2m
-4 + -74m + -24m2 = 2m + -2m

Combine like terms: 2m + -2m = 0
-4 + -74m + -24m2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 37m + 12m2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(2 + 37m + 12m2)' equal to zero and attempt to solve:

Simplifying
2 + 37m + 12m2 = 0

Solving
2 + 37m + 12m2 = 0

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

Divide each side by '12'.
0.1666666667 + 3.083333333m + m2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 3.083333333m + -0.1666666667 + m2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 3.083333333m + m2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 3.083333333m + m2 = 0 + -0.1666666667
3.083333333m + m2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
3.083333333m + m2 = -0.1666666667

The m term is 3.083333333m.  Take half its coefficient (1.541666667).
Square it (2.376736112) and add it to both sides.

Add '2.376736112' to each side of the equation.
3.083333333m + 2.376736112 + m2 = -0.1666666667 + 2.376736112

Reorder the terms:
2.376736112 + 3.083333333m + m2 = -0.1666666667 + 2.376736112

Combine like terms: -0.1666666667 + 2.376736112 = 2.2100694453
2.376736112 + 3.083333333m + m2 = 2.2100694453

Factor a perfect square on the left side:
(m + 1.541666667)(m + 1.541666667) = 2.2100694453

Calculate the square root of the right side: 1.486630232

Break this problem into two subproblems by setting 
(m + 1.541666667) equal to 1.486630232 and -1.486630232.

Subproblem 1
m + 1.541666667 = 1.486630232

Simplifying
m + 1.541666667 = 1.486630232

Reorder the terms:
1.541666667 + m = 1.486630232

Solving
1.541666667 + m = 1.486630232

Solving for variable 'm'.

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

Add '-1.541666667' to each side of the equation.
1.541666667 + -1.541666667 + m = 1.486630232 + -1.541666667

Combine like terms: 1.541666667 + -1.541666667 = 0.000000000
0.000000000 + m = 1.486630232 + -1.541666667
m = 1.486630232 + -1.541666667

Combine like terms: 1.486630232 + -1.541666667 = -0.055036435
m = -0.055036435

Simplifying
m = -0.055036435

Subproblem 2
m + 1.541666667 = -1.486630232

Simplifying
m + 1.541666667 = -1.486630232

Reorder the terms:
1.541666667 + m = -1.486630232

Solving
1.541666667 + m = -1.486630232

Solving for variable 'm'.

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

Add '-1.541666667' to each side of the equation.
1.541666667 + -1.541666667 + m = -1.486630232 + -1.541666667

Combine like terms: 1.541666667 + -1.541666667 = 0.000000000
0.000000000 + m = -1.486630232 + -1.541666667
m = -1.486630232 + -1.541666667

Combine like terms: -1.486630232 + -1.541666667 = -3.028296899
m = -3.028296899

Simplifying
m = -3.028296899

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.055036435, -3.028296899}
Solution
m = {-0.055036435, -3.028296899}