-8m(3m+6)=5

Solution for -8m(3m+6)=5 equation:

Simplifying
-8m(3m + 6) = 5

Reorder the terms:
-8m(6 + 3m) = 5
(6 * -8m + 3m * -8m) = 5
(-48m + -24m2) = 5

Solving
-48m + -24m2 = 5

Solving for variable 'm'.

Reorder the terms:
-5 + -48m + -24m2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -48m + -24m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 48m + 24m2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 48m + 24m2)' equal to zero and attempt to solve:

Simplifying
5 + 48m + 24m2 = 0

Solving
5 + 48m + 24m2 = 0

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

Divide each side by '24'.
0.2083333333 + 2m + m2 = 0

Move the constant term to the right:

Add '-0.2083333333' to each side of the equation.
0.2083333333 + 2m + -0.2083333333 + m2 = 0 + -0.2083333333

Reorder the terms:
0.2083333333 + -0.2083333333 + 2m + m2 = 0 + -0.2083333333

Combine like terms: 0.2083333333 + -0.2083333333 = 0.0000000000
0.0000000000 + 2m + m2 = 0 + -0.2083333333
2m + m2 = 0 + -0.2083333333

Combine like terms: 0 + -0.2083333333 = -0.2083333333
2m + m2 = -0.2083333333

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = -0.2083333333 + 1

Reorder the terms:
1 + 2m + m2 = -0.2083333333 + 1

Combine like terms: -0.2083333333 + 1 = 0.7916666667
1 + 2m + m2 = 0.7916666667

Factor a perfect square on the left side:
(m + 1)(m + 1) = 0.7916666667

Calculate the square root of the right side: 0.889756521

Break this problem into two subproblems by setting 
(m + 1) equal to 0.889756521 and -0.889756521.

Subproblem 1
m + 1 = 0.889756521

Simplifying
m + 1 = 0.889756521

Reorder the terms:
1 + m = 0.889756521

Solving
1 + m = 0.889756521

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = 0.889756521 + -1

Combine like terms: 1 + -1 = 0
0 + m = 0.889756521 + -1
m = 0.889756521 + -1

Combine like terms: 0.889756521 + -1 = -0.110243479
m = -0.110243479

Simplifying
m = -0.110243479

Subproblem 2
m + 1 = -0.889756521

Simplifying
m + 1 = -0.889756521

Reorder the terms:
1 + m = -0.889756521

Solving
1 + m = -0.889756521

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = -0.889756521 + -1

Combine like terms: 1 + -1 = 0
0 + m = -0.889756521 + -1
m = -0.889756521 + -1

Combine like terms: -0.889756521 + -1 = -1.889756521
m = -1.889756521

Simplifying
m = -1.889756521

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.110243479, -1.889756521}
Solution
m = {-0.110243479, -1.889756521}