6m+2(m+7)m=14

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Solution for 6m+2(m+7)m=14 equation: 


Simplifying
6m + 2(m + 7) * m = 14

Reorder the terms:
6m + 2(7 + m) * m = 14

Reorder the terms for easier multiplication:
6m + 2m(7 + m) = 14
6m + (7 * 2m + m * 2m) = 14
6m + (14m + 2m2) = 14

Combine like terms: 6m + 14m = 20m
20m + 2m2 = 14

Solving
20m + 2m2 = 14

Solving for variable 'm'.

Reorder the terms:
-14 + 20m + 2m2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 20m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 10m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 10m + m2)' equal to zero and attempt to solve:

Simplifying
-7 + 10m + m2 = 0

Solving
-7 + 10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 10m + 7 + m2 = 0 + 7

Reorder the terms:
-7 + 7 + 10m + m2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 10m + m2 = 0 + 7
10m + m2 = 0 + 7

Combine like terms: 0 + 7 = 7
10m + m2 = 7

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = 7 + 25

Reorder the terms:
25 + 10m + m2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + 10m + m2 = 32

Factor a perfect square on the left side:
(m + 5)(m + 5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(m + 5) equal to 5.656854249 and -5.656854249.


Subproblem 1
m + 5 = 5.656854249

Simplifying
m + 5 = 5.656854249

Reorder the terms:
5 + m = 5.656854249

Solving
5 + m = 5.656854249

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = 5.656854249 + -5

Combine like terms: 5 + -5 = 0
0 + m = 5.656854249 + -5
m = 5.656854249 + -5

Combine like terms: 5.656854249 + -5 = 0.656854249
m = 0.656854249

Simplifying
m = 0.656854249


Subproblem 2
m + 5 = -5.656854249

Simplifying
m + 5 = -5.656854249

Reorder the terms:
5 + m = -5.656854249

Solving
5 + m = -5.656854249

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = -5.656854249 + -5

Combine like terms: 5 + -5 = 0
0 + m = -5.656854249 + -5
m = -5.656854249 + -5

Combine like terms: -5.656854249 + -5 = -10.656854249
m = -10.656854249

Simplifying
m = -10.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.656854249, -10.656854249}
Solution
m = {0.656854249, -10.656854249}

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