-4m(m+6)=-8

Solution for -4m(m+6)=-8 equation:

Simplifying
-4m(m + 6) = -8

Reorder the terms:
-4m(6 + m) = -8
(6 * -4m + m * -4m) = -8
(-24m + -4m2) = -8

Solving
-24m + -4m2 = -8

Solving for variable 'm'.

Reorder the terms:
8 + -24m + -4m2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + -24m + -4m2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -6m + -1m2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -6m + -1m2)' equal to zero and attempt to solve:

Simplifying
2 + -6m + -1m2 = 0

Solving
2 + -6m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + 6m + m2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6m + 2 + m2 = 0 + 2

Reorder the terms:
-2 + 2 + 6m + m2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6m + m2 = 0 + 2
6m + m2 = 0 + 2

Combine like terms: 0 + 2 = 2
6m + m2 = 2

The m term is 6m.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6m + 9 + m2 = 2 + 9

Reorder the terms:
9 + 6m + m2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + 6m + m2 = 11

Factor a perfect square on the left side:
(m + 3)(m + 3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(m + 3) equal to 3.31662479 and -3.31662479.

Subproblem 1
m + 3 = 3.31662479

Simplifying
m + 3 = 3.31662479

Reorder the terms:
3 + m = 3.31662479

Solving
3 + m = 3.31662479

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -3 + m = 3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + m = 3.31662479 + -3
m = 3.31662479 + -3

Combine like terms: 3.31662479 + -3 = 0.31662479
m = 0.31662479

Simplifying
m = 0.31662479

Subproblem 2
m + 3 = -3.31662479

Simplifying
m + 3 = -3.31662479

Reorder the terms:
3 + m = -3.31662479

Solving
3 + m = -3.31662479

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -3 + m = -3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + m = -3.31662479 + -3
m = -3.31662479 + -3

Combine like terms: -3.31662479 + -3 = -6.31662479
m = -6.31662479

Simplifying
m = -6.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.31662479, -6.31662479}
Solution
m = {0.31662479, -6.31662479}