6(3+3m)m=2

Solution for 6(3+3m)m=2 equation:

Simplifying
6(3 + 3m) * m = 2

Reorder the terms for easier multiplication:
6m(3 + 3m) = 2
(3 * 6m + 3m * 6m) = 2
(18m + 18m2) = 2

Solving
18m + 18m2 = 2

Solving for variable 'm'.

Reorder the terms:
-2 + 18m + 18m2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 18m + 18m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 9m + 9m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 9m + 9m2)' equal to zero and attempt to solve:

Simplifying
-1 + 9m + 9m2 = 0

Solving
-1 + 9m + 9m2 = 0

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

Divide each side by '9'.
-0.1111111111 + m + m2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + m + 0.1111111111 + m2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + m + m2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + m + m2 = 0 + 0.1111111111
m + m2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
m + m2 = 0.1111111111

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 = 0.1111111111 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + m2 = 0.1111111111 + 0.25

Combine like terms: 0.1111111111 + 0.25 = 0.3611111111
1.25 + m2 = 0.3611111111

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 0.3611111111

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(m + 0.5) equal to 0.600925213 and -0.600925213.

Subproblem 1
m + 0.5 = 0.600925213

Simplifying
m + 0.5 = 0.600925213

Reorder the terms:
0.5 + m = 0.600925213

Solving
0.5 + m = 0.600925213

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 = 0.600925213 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 0.600925213 + -0.5
m = 0.600925213 + -0.5

Combine like terms: 0.600925213 + -0.5 = 0.100925213
m = 0.100925213

Simplifying
m = 0.100925213

Subproblem 2
m + 0.5 = -0.600925213

Simplifying
m + 0.5 = -0.600925213

Reorder the terms:
0.5 + m = -0.600925213

Solving
0.5 + m = -0.600925213

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 = -0.600925213 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -0.600925213 + -0.5
m = -0.600925213 + -0.5

Combine like terms: -0.600925213 + -0.5 = -1.100925213
m = -1.100925213

Simplifying
m = -1.100925213

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.100925213, -1.100925213}
Solution
m = {0.100925213, -1.100925213}