5m(4m+3)=2m+6

Solution for 5m(4m+3)=2m+6 equation:

Simplifying
5m(4m + 3) = 2m + 6

Reorder the terms:
5m(3 + 4m) = 2m + 6
(3 * 5m + 4m * 5m) = 2m + 6
(15m + 20m2) = 2m + 6

Reorder the terms:
15m + 20m2 = 6 + 2m

Solving
15m + 20m2 = 6 + 2m

Solving for variable 'm'.

Reorder the terms:
-6 + 15m + -2m + 20m2 = 6 + 2m + -6 + -2m

Combine like terms: 15m + -2m = 13m
-6 + 13m + 20m2 = 6 + 2m + -6 + -2m

Reorder the terms:
-6 + 13m + 20m2 = 6 + -6 + 2m + -2m

Combine like terms: 6 + -6 = 0
-6 + 13m + 20m2 = 0 + 2m + -2m
-6 + 13m + 20m2 = 2m + -2m

Combine like terms: 2m + -2m = 0
-6 + 13m + 20m2 = 0

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

Divide each side by '20'.
-0.3 + 0.65m + m2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 0.65m + 0.3 + m2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 0.65m + m2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 0.65m + m2 = 0.0 + 0.3
0.65m + m2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
0.65m + m2 = 0.3

The m term is 0.65m.  Take half its coefficient (0.325).
Square it (0.105625) and add it to both sides.

Add '0.105625' to each side of the equation.
0.65m + 0.105625 + m2 = 0.3 + 0.105625

Reorder the terms:
0.105625 + 0.65m + m2 = 0.3 + 0.105625

Combine like terms: 0.3 + 0.105625 = 0.405625
0.105625 + 0.65m + m2 = 0.405625

Factor a perfect square on the left side:
(m + 0.325)(m + 0.325) = 0.405625

Calculate the square root of the right side: 0.63688696

Break this problem into two subproblems by setting 
(m + 0.325) equal to 0.63688696 and -0.63688696.

Subproblem 1
m + 0.325 = 0.63688696

Simplifying
m + 0.325 = 0.63688696

Reorder the terms:
0.325 + m = 0.63688696

Solving
0.325 + m = 0.63688696

Solving for variable 'm'.

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

Add '-0.325' to each side of the equation.
0.325 + -0.325 + m = 0.63688696 + -0.325

Combine like terms: 0.325 + -0.325 = 0.000
0.000 + m = 0.63688696 + -0.325
m = 0.63688696 + -0.325

Combine like terms: 0.63688696 + -0.325 = 0.31188696
m = 0.31188696

Simplifying
m = 0.31188696

Subproblem 2
m + 0.325 = -0.63688696

Simplifying
m + 0.325 = -0.63688696

Reorder the terms:
0.325 + m = -0.63688696

Solving
0.325 + m = -0.63688696

Solving for variable 'm'.

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

Add '-0.325' to each side of the equation.
0.325 + -0.325 + m = -0.63688696 + -0.325

Combine like terms: 0.325 + -0.325 = 0.000
0.000 + m = -0.63688696 + -0.325
m = -0.63688696 + -0.325

Combine like terms: -0.63688696 + -0.325 = -0.96188696
m = -0.96188696

Simplifying
m = -0.96188696

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.31188696, -0.96188696}