11(2m+2)-6=4m(3m-2)

Solution for 11(2m+2)-6=4m(3m-2) equation:

Simplifying
11(2m + 2) + -6 = 4m(3m + -2)

Reorder the terms:
11(2 + 2m) + -6 = 4m(3m + -2)
(2 * 11 + 2m * 11) + -6 = 4m(3m + -2)
(22 + 22m) + -6 = 4m(3m + -2)

Reorder the terms:
22 + -6 + 22m = 4m(3m + -2)

Combine like terms: 22 + -6 = 16
16 + 22m = 4m(3m + -2)

Reorder the terms:
16 + 22m = 4m(-2 + 3m)
16 + 22m = (-2 * 4m + 3m * 4m)
16 + 22m = (-8m + 12m2)

Solving
16 + 22m = -8m + 12m2

Solving for variable 'm'.

Combine like terms: 22m + 8m = 30m
16 + 30m + -12m2 = -8m + 12m2 + 8m + -12m2

Reorder the terms:
16 + 30m + -12m2 = -8m + 8m + 12m2 + -12m2

Combine like terms: -8m + 8m = 0
16 + 30m + -12m2 = 0 + 12m2 + -12m2
16 + 30m + -12m2 = 12m2 + -12m2

Combine like terms: 12m2 + -12m2 = 0
16 + 30m + -12m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 15m + -6m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 15m + -6m2)' equal to zero and attempt to solve:

Simplifying
8 + 15m + -6m2 = 0

Solving
8 + 15m + -6m2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.333333333 + -2.5m + m2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2.5m + 1.333333333 + m2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2.5m + m2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2.5m + m2 = 0 + 1.333333333
-2.5m + m2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2.5m + m2 = 1.333333333

The m term is -2.5m.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5m + 1.5625 + m2 = 1.333333333 + 1.5625

Reorder the terms:
1.5625 + -2.5m + m2 = 1.333333333 + 1.5625

Combine like terms: 1.333333333 + 1.5625 = 2.895833333
1.5625 + -2.5m + m2 = 2.895833333

Factor a perfect square on the left side:
(m + -1.25)(m + -1.25) = 2.895833333

Calculate the square root of the right side: 1.701714821

Break this problem into two subproblems by setting 
(m + -1.25) equal to 1.701714821 and -1.701714821.

Subproblem 1
m + -1.25 = 1.701714821

Simplifying
m + -1.25 = 1.701714821

Reorder the terms:
-1.25 + m = 1.701714821

Solving
-1.25 + m = 1.701714821

Solving for variable 'm'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + m = 1.701714821 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + m = 1.701714821 + 1.25
m = 1.701714821 + 1.25

Combine like terms: 1.701714821 + 1.25 = 2.951714821
m = 2.951714821

Simplifying
m = 2.951714821

Subproblem 2
m + -1.25 = -1.701714821

Simplifying
m + -1.25 = -1.701714821

Reorder the terms:
-1.25 + m = -1.701714821

Solving
-1.25 + m = -1.701714821

Solving for variable 'm'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + m = -1.701714821 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + m = -1.701714821 + 1.25
m = -1.701714821 + 1.25

Combine like terms: -1.701714821 + 1.25 = -0.451714821
m = -0.451714821

Simplifying
m = -0.451714821

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.951714821, -0.451714821}
Solution
m = {2.951714821, -0.451714821}