2(m+7)-3(m+1)=4(m-7)m

Solution for 2(m+7)-3(m+1)=4(m-7)m equation:

Simplifying
2(m + 7) + -3(m + 1) = 4(m + -7) * m

Reorder the terms:
2(7 + m) + -3(m + 1) = 4(m + -7) * m
(7 * 2 + m * 2) + -3(m + 1) = 4(m + -7) * m
(14 + 2m) + -3(m + 1) = 4(m + -7) * m

Reorder the terms:
14 + 2m + -3(1 + m) = 4(m + -7) * m
14 + 2m + (1 * -3 + m * -3) = 4(m + -7) * m
14 + 2m + (-3 + -3m) = 4(m + -7) * m

Reorder the terms:
14 + -3 + 2m + -3m = 4(m + -7) * m

Combine like terms: 14 + -3 = 11
11 + 2m + -3m = 4(m + -7) * m

Combine like terms: 2m + -3m = -1m
11 + -1m = 4(m + -7) * m

Reorder the terms:
11 + -1m = 4(-7 + m) * m

Reorder the terms for easier multiplication:
11 + -1m = 4m(-7 + m)
11 + -1m = (-7 * 4m + m * 4m)
11 + -1m = (-28m + 4m2)

Solving
11 + -1m = -28m + 4m2

Solving for variable 'm'.

Combine like terms: -1m + 28m = 27m
11 + 27m + -4m2 = -28m + 4m2 + 28m + -4m2

Reorder the terms:
11 + 27m + -4m2 = -28m + 28m + 4m2 + -4m2

Combine like terms: -28m + 28m = 0
11 + 27m + -4m2 = 0 + 4m2 + -4m2
11 + 27m + -4m2 = 4m2 + -4m2

Combine like terms: 4m2 + -4m2 = 0
11 + 27m + -4m2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.75 + -6.75m + m2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -6.75m + 2.75 + m2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -6.75m + m2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -6.75m + m2 = 0 + 2.75
-6.75m + m2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-6.75m + m2 = 2.75

The m term is -6.75m.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75m + 11.390625 + m2 = 2.75 + 11.390625

Reorder the terms:
11.390625 + -6.75m + m2 = 2.75 + 11.390625

Combine like terms: 2.75 + 11.390625 = 14.140625
11.390625 + -6.75m + m2 = 14.140625

Factor a perfect square on the left side:
(m + -3.375)(m + -3.375) = 14.140625

Calculate the square root of the right side: 3.760402239

Break this problem into two subproblems by setting 
(m + -3.375) equal to 3.760402239 and -3.760402239.

Subproblem 1
m + -3.375 = 3.760402239

Simplifying
m + -3.375 = 3.760402239

Reorder the terms:
-3.375 + m = 3.760402239

Solving
-3.375 + m = 3.760402239

Solving for variable 'm'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + m = 3.760402239 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + m = 3.760402239 + 3.375
m = 3.760402239 + 3.375

Combine like terms: 3.760402239 + 3.375 = 7.135402239
m = 7.135402239

Simplifying
m = 7.135402239

Subproblem 2
m + -3.375 = -3.760402239

Simplifying
m + -3.375 = -3.760402239

Reorder the terms:
-3.375 + m = -3.760402239

Solving
-3.375 + m = -3.760402239

Solving for variable 'm'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + m = -3.760402239 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + m = -3.760402239 + 3.375
m = -3.760402239 + 3.375

Combine like terms: -3.760402239 + 3.375 = -0.385402239
m = -0.385402239

Simplifying
m = -0.385402239

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {7.135402239, -0.385402239}