3m-2m(m+7)=2m+14

Solution for 3m-2m(m+7)=2m+14 equation:

Simplifying
3m + -2m(m + 7) = 2m + 14

Reorder the terms:
3m + -2m(7 + m) = 2m + 14
3m + (7 * -2m + m * -2m) = 2m + 14
3m + (-14m + -2m2) = 2m + 14

Combine like terms: 3m + -14m = -11m
-11m + -2m2 = 2m + 14

Reorder the terms:
-11m + -2m2 = 14 + 2m

Solving
-11m + -2m2 = 14 + 2m

Solving for variable 'm'.

Reorder the terms:
-14 + -11m + -2m + -2m2 = 14 + 2m + -14 + -2m

Combine like terms: -11m + -2m = -13m
-14 + -13m + -2m2 = 14 + 2m + -14 + -2m

Reorder the terms:
-14 + -13m + -2m2 = 14 + -14 + 2m + -2m

Combine like terms: 14 + -14 = 0
-14 + -13m + -2m2 = 0 + 2m + -2m
-14 + -13m + -2m2 = 2m + -2m

Combine like terms: 2m + -2m = 0
-14 + -13m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 13m + 2m2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(14 + 13m + 2m2)' equal to zero and attempt to solve:

Simplifying
14 + 13m + 2m2 = 0

Solving
14 + 13m + 2m2 = 0

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

Divide each side by '2'.
7 + 6.5m + m2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6.5m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + 6.5m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6.5m + m2 = 0 + -7
6.5m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
6.5m + m2 = -7

The m term is 6.5m.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5m + 10.5625 + m2 = -7 + 10.5625

Reorder the terms:
10.5625 + 6.5m + m2 = -7 + 10.5625

Combine like terms: -7 + 10.5625 = 3.5625
10.5625 + 6.5m + m2 = 3.5625

Factor a perfect square on the left side:
(m + 3.25)(m + 3.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(m + 3.25) equal to 1.887458609 and -1.887458609.

Subproblem 1
m + 3.25 = 1.887458609

Simplifying
m + 3.25 = 1.887458609

Reorder the terms:
3.25 + m = 1.887458609

Solving
3.25 + m = 1.887458609

Solving for variable 'm'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + m = 1.887458609 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + m = 1.887458609 + -3.25
m = 1.887458609 + -3.25

Combine like terms: 1.887458609 + -3.25 = -1.362541391
m = -1.362541391

Simplifying
m = -1.362541391

Subproblem 2
m + 3.25 = -1.887458609

Simplifying
m + 3.25 = -1.887458609

Reorder the terms:
3.25 + m = -1.887458609

Solving
3.25 + m = -1.887458609

Solving for variable 'm'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + m = -1.887458609 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + m = -1.887458609 + -3.25
m = -1.887458609 + -3.25

Combine like terms: -1.887458609 + -3.25 = -5.137458609
m = -5.137458609

Simplifying
m = -5.137458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.362541391, -5.137458609}
Solution
m = {-1.362541391, -5.137458609}