-4m(m+12)=36

Solution for -4m(m+12)=36 equation:

Simplifying
-4m(m + 12) = 36

Reorder the terms:
-4m(12 + m) = 36
(12 * -4m + m * -4m) = 36
(-48m + -4m2) = 36

Solving
-48m + -4m2 = 36

Solving for variable 'm'.

Reorder the terms:
-36 + -48m + -4m2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -48m + -4m2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(9 + 12m + m2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(9 + 12m + m2)' equal to zero and attempt to solve:

Simplifying
9 + 12m + m2 = 0

Solving
9 + 12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 12m + -9 + m2 = 0 + -9

Reorder the terms:
9 + -9 + 12m + m2 = 0 + -9

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

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

The m term is 12m.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12m + 36 + m2 = -9 + 36

Reorder the terms:
36 + 12m + m2 = -9 + 36

Combine like terms: -9 + 36 = 27
36 + 12m + m2 = 27

Factor a perfect square on the left side:
(m + 6)(m + 6) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(m + 6) equal to 5.196152423 and -5.196152423.

Subproblem 1
m + 6 = 5.196152423

Simplifying
m + 6 = 5.196152423

Reorder the terms:
6 + m = 5.196152423

Solving
6 + m = 5.196152423

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = 5.196152423 + -6

Combine like terms: 6 + -6 = 0
0 + m = 5.196152423 + -6
m = 5.196152423 + -6

Combine like terms: 5.196152423 + -6 = -0.803847577
m = -0.803847577

Simplifying
m = -0.803847577

Subproblem 2
m + 6 = -5.196152423

Simplifying
m + 6 = -5.196152423

Reorder the terms:
6 + m = -5.196152423

Solving
6 + m = -5.196152423

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = -5.196152423 + -6

Combine like terms: 6 + -6 = 0
0 + m = -5.196152423 + -6
m = -5.196152423 + -6

Combine like terms: -5.196152423 + -6 = -11.196152423
m = -11.196152423

Simplifying
m = -11.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.803847577, -11.196152423}
Solution
m = {-0.803847577, -11.196152423}