6m^2+2m=10

Solution for 6m^2+2m=10 equation:

Simplifying
6m2 + 2m = 10

Reorder the terms:
2m + 6m2 = 10

Solving
2m + 6m2 = 10

Solving for variable 'm'.

Reorder the terms:
-10 + 2m + 6m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 2m + 6m2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + m + 3m2)' equal to zero and attempt to solve:

Simplifying
-5 + m + 3m2 = 0

Solving
-5 + m + 3m2 = 0

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

Divide each side by '3'.
-1.666666667 + 0.3333333333m + m2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.3333333333m + 1.666666667 + m2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.3333333333m + m2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.3333333333m + m2 = 0 + 1.666666667
0.3333333333m + m2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.3333333333m + m2 = 1.666666667

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.
0.3333333333m + 0.25 + m2 = 1.666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333m + m2 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + 0.3333333333m + m2 = 1.916666667

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(m + 0.5) equal to 1.384437311 and -1.384437311.

Subproblem 1
m + 0.5 = 1.384437311

Simplifying
m + 0.5 = 1.384437311

Reorder the terms:
0.5 + m = 1.384437311

Solving
0.5 + m = 1.384437311

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 = 1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 1.384437311 + -0.5
m = 1.384437311 + -0.5

Combine like terms: 1.384437311 + -0.5 = 0.884437311
m = 0.884437311

Simplifying
m = 0.884437311

Subproblem 2
m + 0.5 = -1.384437311

Simplifying
m + 0.5 = -1.384437311

Reorder the terms:
0.5 + m = -1.384437311

Solving
0.5 + m = -1.384437311

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 = -1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -1.384437311 + -0.5
m = -1.384437311 + -0.5

Combine like terms: -1.384437311 + -0.5 = -1.884437311
m = -1.884437311

Simplifying
m = -1.884437311

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.884437311, -1.884437311}
Solution
m = {0.884437311, -1.884437311}