2m(m+3)-6(3m-2)+2=0

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Solution for 2m(m+3)-6(3m-2)+2=0 equation: 


Simplifying
2m(m + 3) + -6(3m + -2) + 2 = 0

Reorder the terms:
2m(3 + m) + -6(3m + -2) + 2 = 0
(3 * 2m + m * 2m) + -6(3m + -2) + 2 = 0
(6m + 2m2) + -6(3m + -2) + 2 = 0

Reorder the terms:
6m + 2m2 + -6(-2 + 3m) + 2 = 0
6m + 2m2 + (-2 * -6 + 3m * -6) + 2 = 0
6m + 2m2 + (12 + -18m) + 2 = 0

Reorder the terms:
12 + 2 + 6m + -18m + 2m2 = 0

Combine like terms: 12 + 2 = 14
14 + 6m + -18m + 2m2 = 0

Combine like terms: 6m + -18m = -12m
14 + -12m + 2m2 = 0

Solving
14 + -12m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -6m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -6m + m2)' equal to zero and attempt to solve:

Simplifying
7 + -6m + m2 = 0

Solving
7 + -6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + -6m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6m + m2 = 0 + -7
-6m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6m + m2 = -7

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = -7 + 9

Reorder the terms:
9 + -6m + m2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6m + m2 = 2

Factor a perfect square on the left side:
(m + -3)(m + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(m + -3) equal to 1.414213562 and -1.414213562.


Subproblem 1
m + -3 = 1.414213562

Simplifying
m + -3 = 1.414213562

Reorder the terms:
-3 + m = 1.414213562

Solving
-3 + m = 1.414213562

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + m = 1.414213562 + 3
m = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
m = 4.414213562

Simplifying
m = 4.414213562


Subproblem 2
m + -3 = -1.414213562

Simplifying
m + -3 = -1.414213562

Reorder the terms:
-3 + m = -1.414213562

Solving
-3 + m = -1.414213562

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + m = -1.414213562 + 3
m = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
m = 1.585786438

Simplifying
m = 1.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.414213562, 1.585786438}
Solution
m = {4.414213562, 1.585786438}

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