3m(2m+14)=10

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Solution for 3m(2m+14)=10 equation: 


Simplifying
3m(2m + 14) = 10

Reorder the terms:
3m(14 + 2m) = 10
(14 * 3m + 2m * 3m) = 10
(42m + 6m2) = 10

Solving
42m + 6m2 = 10

Solving for variable 'm'.

Reorder the terms:
-10 + 42m + 6m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 42m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 21m + 3m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 21m + 3m2)' equal to zero and attempt to solve:

Simplifying
-5 + 21m + 3m2 = 0

Solving
-5 + 21m + 3m2 = 0

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

Divide each side by '3'.
-1.666666667 + 7m + m2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 7m + 1.666666667 + m2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 7m + m2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 7m + m2 = 0 + 1.666666667
7m + m2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
7m + m2 = 1.666666667

The m term is 7m.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7m + 12.25 + m2 = 1.666666667 + 12.25

Reorder the terms:
12.25 + 7m + m2 = 1.666666667 + 12.25

Combine like terms: 1.666666667 + 12.25 = 13.916666667
12.25 + 7m + m2 = 13.916666667

Factor a perfect square on the left side:
(m + 3.5)(m + 3.5) = 13.916666667

Calculate the square root of the right side: 3.730504881

Break this problem into two subproblems by setting 
(m + 3.5) equal to 3.730504881 and -3.730504881.


Subproblem 1
m + 3.5 = 3.730504881

Simplifying
m + 3.5 = 3.730504881

Reorder the terms:
3.5 + m = 3.730504881

Solving
3.5 + m = 3.730504881

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = 3.730504881 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = 3.730504881 + -3.5
m = 3.730504881 + -3.5

Combine like terms: 3.730504881 + -3.5 = 0.230504881
m = 0.230504881

Simplifying
m = 0.230504881


Subproblem 2
m + 3.5 = -3.730504881

Simplifying
m + 3.5 = -3.730504881

Reorder the terms:
3.5 + m = -3.730504881

Solving
3.5 + m = -3.730504881

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = -3.730504881 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = -3.730504881 + -3.5
m = -3.730504881 + -3.5

Combine like terms: -3.730504881 + -3.5 = -7.230504881
m = -7.230504881

Simplifying
m = -7.230504881


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.230504881, -7.230504881}
Solution
m = {0.230504881, -7.230504881}

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