3(m-4)2m=m+8

Solution for 3(m-4)2m=m+8 equation:

Simplifying
3(m + -4) * 2m = m + 8

Reorder the terms:
3(-4 + m) * 2m = m + 8

Reorder the terms for easier multiplication:
3 * 2m(-4 + m) = m + 8

Multiply 3 * 2
6m(-4 + m) = m + 8
(-4 * 6m + m * 6m) = m + 8
(-24m + 6m2) = m + 8

Reorder the terms:
-24m + 6m2 = 8 + m

Solving
-24m + 6m2 = 8 + m

Solving for variable 'm'.

Reorder the terms:
-8 + -24m + -1m + 6m2 = 8 + m + -8 + -1m

Combine like terms: -24m + -1m = -25m
-8 + -25m + 6m2 = 8 + m + -8 + -1m

Reorder the terms:
-8 + -25m + 6m2 = 8 + -8 + m + -1m

Combine like terms: 8 + -8 = 0
-8 + -25m + 6m2 = 0 + m + -1m
-8 + -25m + 6m2 = m + -1m

Combine like terms: m + -1m = 0
-8 + -25m + 6m2 = 0

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

Divide each side by '6'.
-1.333333333 + -4.166666667m + m2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -4.166666667m + 1.333333333 + m2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -4.166666667m + m2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -4.166666667m + m2 = 0 + 1.333333333
-4.166666667m + m2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-4.166666667m + m2 = 1.333333333

The m term is -4.166666667m.  Take half its coefficient (-2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
-4.166666667m + 4.340277781 + m2 = 1.333333333 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667m + m2 = 1.333333333 + 4.340277781

Combine like terms: 1.333333333 + 4.340277781 = 5.673611114
4.340277781 + -4.166666667m + m2 = 5.673611114

Factor a perfect square on the left side:
(m + -2.083333334)(m + -2.083333334) = 5.673611114

Calculate the square root of the right side: 2.381934322

Break this problem into two subproblems by setting 
(m + -2.083333334) equal to 2.381934322 and -2.381934322.

Subproblem 1
m + -2.083333334 = 2.381934322

Simplifying
m + -2.083333334 = 2.381934322

Reorder the terms:
-2.083333334 + m = 2.381934322

Solving
-2.083333334 + m = 2.381934322

Solving for variable 'm'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + m = 2.381934322 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + m = 2.381934322 + 2.083333334
m = 2.381934322 + 2.083333334

Combine like terms: 2.381934322 + 2.083333334 = 4.465267656
m = 4.465267656

Simplifying
m = 4.465267656

Subproblem 2
m + -2.083333334 = -2.381934322

Simplifying
m + -2.083333334 = -2.381934322

Reorder the terms:
-2.083333334 + m = -2.381934322

Solving
-2.083333334 + m = -2.381934322

Solving for variable 'm'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + m = -2.381934322 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + m = -2.381934322 + 2.083333334
m = -2.381934322 + 2.083333334

Combine like terms: -2.381934322 + 2.083333334 = -0.298600988
m = -0.298600988

Simplifying
m = -0.298600988

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.465267656, -0.298600988}