3m(m+6)=6(m-1)

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

Simplifying
3m(m + 6) = 6(m + -1)

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

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

Solving
18m + 3m2 = -6 + 6m

Solving for variable 'm'.

Reorder the terms:
6 + 18m + -6m + 3m2 = -6 + 6m + 6 + -6m

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

Reorder the terms:
6 + 12m + 3m2 = -6 + 6 + 6m + -6m

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 4m + m2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 4m + m2)' equal to zero and attempt to solve:

Simplifying
2 + 4m + m2 = 0

Solving
2 + 4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 4m + -2 + m2 = 0 + -2

Reorder the terms:
2 + -2 + 4m + m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4m + m2 = 0 + -2
4m + m2 = 0 + -2

Combine like terms: 0 + -2 = -2
4m + m2 = -2

The m term is 4m.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4m + 4 + m2 = -2 + 4

Reorder the terms:
4 + 4m + m2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + 4m + m2 = 2

Factor a perfect square on the left side:
(m + 2)(m + 2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(m + 2) equal to 1.414213562 and -1.414213562.

Subproblem 1
m + 2 = 1.414213562

Simplifying
m + 2 = 1.414213562

Reorder the terms:
2 + m = 1.414213562

Solving
2 + m = 1.414213562

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = 1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + m = 1.414213562 + -2
m = 1.414213562 + -2

Combine like terms: 1.414213562 + -2 = -0.585786438
m = -0.585786438

Simplifying
m = -0.585786438

Subproblem 2
m + 2 = -1.414213562

Simplifying
m + 2 = -1.414213562

Reorder the terms:
2 + m = -1.414213562

Solving
2 + m = -1.414213562

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = -1.414213562 + -2

Combine like terms: 2 + -2 = 0
0 + m = -1.414213562 + -2
m = -1.414213562 + -2

Combine like terms: -1.414213562 + -2 = -3.414213562
m = -3.414213562

Simplifying
m = -3.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.585786438, -3.414213562}
Solution
m = {-0.585786438, -3.414213562}