12m^2+2m-8=0

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Solution for 12m^2+2m-8=0 equation: 


Simplifying
12m2 + 2m + -8 = 0

Reorder the terms:
-8 + 2m + 12m2 = 0

Solving
-8 + 2m + 12m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + m + 6m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + m + 6m2)' equal to zero and attempt to solve:

Simplifying
-4 + m + 6m2 = 0

Solving
-4 + m + 6m2 = 0

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

Divide each side by '6'.
-0.6666666667 + 0.1666666667m + m2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.1666666667m + 0.6666666667 + m2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.1666666667m + m2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.1666666667m + m2 = 0 + 0.6666666667
0.1666666667m + m2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.1666666667m + m2 = 0.6666666667

The m term is m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667m + 0.25 + m2 = 0.6666666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667m + m2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
0.25 + 0.1666666667m + m2 = 0.9166666667

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(m + 0.5) equal to 0.957427108 and -0.957427108.


Subproblem 1
m + 0.5 = 0.957427108

Simplifying
m + 0.5 = 0.957427108

Reorder the terms:
0.5 + m = 0.957427108

Solving
0.5 + m = 0.957427108

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = 0.957427108 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 0.957427108 + -0.5
m = 0.957427108 + -0.5

Combine like terms: 0.957427108 + -0.5 = 0.457427108
m = 0.457427108

Simplifying
m = 0.457427108


Subproblem 2
m + 0.5 = -0.957427108

Simplifying
m + 0.5 = -0.957427108

Reorder the terms:
0.5 + m = -0.957427108

Solving
0.5 + m = -0.957427108

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = -0.957427108 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -0.957427108 + -0.5
m = -0.957427108 + -0.5

Combine like terms: -0.957427108 + -0.5 = -1.457427108
m = -1.457427108

Simplifying
m = -1.457427108


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.457427108, -1.457427108}
Solution
m = {0.457427108, -1.457427108}

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