6(1+3m)=-8m(-2m+5)-4

Solution for 6(1+3m)=-8m(-2m+5)-4 equation:

Simplifying
6(1 + 3m) = -8m(-2m + 5) + -4
(1 * 6 + 3m * 6) = -8m(-2m + 5) + -4
(6 + 18m) = -8m(-2m + 5) + -4

Reorder the terms:
6 + 18m = -8m(5 + -2m) + -4
6 + 18m = (5 * -8m + -2m * -8m) + -4
6 + 18m = (-40m + 16m2) + -4

Reorder the terms:
6 + 18m = -4 + -40m + 16m2

Solving
6 + 18m = -4 + -40m + 16m2

Solving for variable 'm'.

Reorder the terms:
6 + 4 + 18m + 40m + -16m2 = -4 + -40m + 16m2 + 4 + 40m + -16m2

Combine like terms: 6 + 4 = 10
10 + 18m + 40m + -16m2 = -4 + -40m + 16m2 + 4 + 40m + -16m2

Combine like terms: 18m + 40m = 58m
10 + 58m + -16m2 = -4 + -40m + 16m2 + 4 + 40m + -16m2

Reorder the terms:
10 + 58m + -16m2 = -4 + 4 + -40m + 40m + 16m2 + -16m2

Combine like terms: -4 + 4 = 0
10 + 58m + -16m2 = 0 + -40m + 40m + 16m2 + -16m2
10 + 58m + -16m2 = -40m + 40m + 16m2 + -16m2

Combine like terms: -40m + 40m = 0
10 + 58m + -16m2 = 0 + 16m2 + -16m2
10 + 58m + -16m2 = 16m2 + -16m2

Combine like terms: 16m2 + -16m2 = 0
10 + 58m + -16m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 29m + -8m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 29m + -8m2)' equal to zero and attempt to solve:

Simplifying
5 + 29m + -8m2 = 0

Solving
5 + 29m + -8m2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.625 + -3.625m + m2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -3.625m + 0.625 + m2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -3.625m + m2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -3.625m + m2 = 0 + 0.625
-3.625m + m2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-3.625m + m2 = 0.625

The m term is -3.625m.  Take half its coefficient (-1.8125).
Square it (3.28515625) and add it to both sides.

Add '3.28515625' to each side of the equation.
-3.625m + 3.28515625 + m2 = 0.625 + 3.28515625

Reorder the terms:
3.28515625 + -3.625m + m2 = 0.625 + 3.28515625

Combine like terms: 0.625 + 3.28515625 = 3.91015625
3.28515625 + -3.625m + m2 = 3.91015625

Factor a perfect square on the left side:
(m + -1.8125)(m + -1.8125) = 3.91015625

Calculate the square root of the right side: 1.977411502

Break this problem into two subproblems by setting 
(m + -1.8125) equal to 1.977411502 and -1.977411502.

Subproblem 1
m + -1.8125 = 1.977411502

Simplifying
m + -1.8125 = 1.977411502

Reorder the terms:
-1.8125 + m = 1.977411502

Solving
-1.8125 + m = 1.977411502

Solving for variable 'm'.

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

Add '1.8125' to each side of the equation.
-1.8125 + 1.8125 + m = 1.977411502 + 1.8125

Combine like terms: -1.8125 + 1.8125 = 0.0000
0.0000 + m = 1.977411502 + 1.8125
m = 1.977411502 + 1.8125

Combine like terms: 1.977411502 + 1.8125 = 3.789911502
m = 3.789911502

Simplifying
m = 3.789911502

Subproblem 2
m + -1.8125 = -1.977411502

Simplifying
m + -1.8125 = -1.977411502

Reorder the terms:
-1.8125 + m = -1.977411502

Solving
-1.8125 + m = -1.977411502

Solving for variable 'm'.

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

Add '1.8125' to each side of the equation.
-1.8125 + 1.8125 + m = -1.977411502 + 1.8125

Combine like terms: -1.8125 + 1.8125 = 0.0000
0.0000 + m = -1.977411502 + 1.8125
m = -1.977411502 + 1.8125

Combine like terms: -1.977411502 + 1.8125 = -0.164911502
m = -0.164911502

Simplifying
m = -0.164911502

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.789911502, -0.164911502}
Solution
m = {3.789911502, -0.164911502}