3(2m+5)2m=2

Solution for 3(2m+5)2m=2 equation:

Simplifying
3(2m + 5) * 2m = 2

Reorder the terms:
3(5 + 2m) * 2m = 2

Reorder the terms for easier multiplication:
3 * 2m(5 + 2m) = 2

Multiply 3 * 2
6m(5 + 2m) = 2
(5 * 6m + 2m * 6m) = 2
(30m + 12m2) = 2

Solving
30m + 12m2 = 2

Solving for variable 'm'.

Reorder the terms:
-2 + 30m + 12m2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 30m + 12m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 15m + 6m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 15m + 6m2)' equal to zero and attempt to solve:

Simplifying
-1 + 15m + 6m2 = 0

Solving
-1 + 15m + 6m2 = 0

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

Divide each side by '6'.
-0.1666666667 + 2.5m + m2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 2.5m + 0.1666666667 + m2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 2.5m + m2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 2.5m + m2 = 0 + 0.1666666667
2.5m + m2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
2.5m + m2 = 0.1666666667

The m term is 2.5m.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5m + 1.5625 + m2 = 0.1666666667 + 1.5625

Reorder the terms:
1.5625 + 2.5m + m2 = 0.1666666667 + 1.5625

Combine like terms: 0.1666666667 + 1.5625 = 1.7291666667
1.5625 + 2.5m + m2 = 1.7291666667

Factor a perfect square on the left side:
(m + 1.25)(m + 1.25) = 1.7291666667

Calculate the square root of the right side: 1.31497782

Break this problem into two subproblems by setting 
(m + 1.25) equal to 1.31497782 and -1.31497782.

Subproblem 1
m + 1.25 = 1.31497782

Simplifying
m + 1.25 = 1.31497782

Reorder the terms:
1.25 + m = 1.31497782

Solving
1.25 + m = 1.31497782

Solving for variable 'm'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + m = 1.31497782 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + m = 1.31497782 + -1.25
m = 1.31497782 + -1.25

Combine like terms: 1.31497782 + -1.25 = 0.06497782
m = 0.06497782

Simplifying
m = 0.06497782

Subproblem 2
m + 1.25 = -1.31497782

Simplifying
m + 1.25 = -1.31497782

Reorder the terms:
1.25 + m = -1.31497782

Solving
1.25 + m = -1.31497782

Solving for variable 'm'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + m = -1.31497782 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + m = -1.31497782 + -1.25
m = -1.31497782 + -1.25

Combine like terms: -1.31497782 + -1.25 = -2.56497782
m = -2.56497782

Simplifying
m = -2.56497782

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.06497782, -2.56497782}
Solution
m = {0.06497782, -2.56497782}