3m(3m+6)-3(m^2+4m+1)=

Solution for 3m(3m+6)-3(m^2+4m+1)= equation:

Simplifying
3m(3m + 6) + -3(m2 + 4m + 1) = 0

Reorder the terms:
3m(6 + 3m) + -3(m2 + 4m + 1) = 0
(6 * 3m + 3m * 3m) + -3(m2 + 4m + 1) = 0
(18m + 9m2) + -3(m2 + 4m + 1) = 0

Reorder the terms:
18m + 9m2 + -3(1 + 4m + m2) = 0
18m + 9m2 + (1 * -3 + 4m * -3 + m2 * -3) = 0
18m + 9m2 + (-3 + -12m + -3m2) = 0

Reorder the terms:
-3 + 18m + -12m + 9m2 + -3m2 = 0

Combine like terms: 18m + -12m = 6m
-3 + 6m + 9m2 + -3m2 = 0

Combine like terms: 9m2 + -3m2 = 6m2
-3 + 6m + 6m2 = 0

Solving
-3 + 6m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2m + 2m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 2m + 2m2)' equal to zero and attempt to solve:

Simplifying
-1 + 2m + 2m2 = 0

Solving
-1 + 2m + 2m2 = 0

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

Divide each side by '2'.
-0.5 + m + m2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + m + 0.5 + m2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + m + m2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m + m2 = 0 + 0.5
m + m2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
m + m2 = 0.5

The m term is m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + m2 = 0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + m2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
1.25 + m2 = 0.75

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(m + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
m + 0.5 = 0.866025404

Simplifying
m + 0.5 = 0.866025404

Reorder the terms:
0.5 + m = 0.866025404

Solving
0.5 + m = 0.866025404

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 0.866025404 + -0.5
m = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
m = 0.366025404

Simplifying
m = 0.366025404

Subproblem 2
m + 0.5 = -0.866025404

Simplifying
m + 0.5 = -0.866025404

Reorder the terms:
0.5 + m = -0.866025404

Solving
0.5 + m = -0.866025404

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -0.866025404 + -0.5
m = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
m = -1.366025404

Simplifying
m = -1.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.366025404, -1.366025404}
Solution
m = {0.366025404, -1.366025404}