2(3+m)m=9(5m-10)

Solution for 2(3+m)m=9(5m-10) equation:

Simplifying
2(3 + m) * m = 9(5m + -10)

Reorder the terms for easier multiplication:
2m(3 + m) = 9(5m + -10)
(3 * 2m + m * 2m) = 9(5m + -10)
(6m + 2m2) = 9(5m + -10)

Reorder the terms:
6m + 2m2 = 9(-10 + 5m)
6m + 2m2 = (-10 * 9 + 5m * 9)
6m + 2m2 = (-90 + 45m)

Solving
6m + 2m2 = -90 + 45m

Solving for variable 'm'.

Reorder the terms:
90 + 6m + -45m + 2m2 = -90 + 45m + 90 + -45m

Combine like terms: 6m + -45m = -39m
90 + -39m + 2m2 = -90 + 45m + 90 + -45m

Reorder the terms:
90 + -39m + 2m2 = -90 + 90 + 45m + -45m

Combine like terms: -90 + 90 = 0
90 + -39m + 2m2 = 0 + 45m + -45m
90 + -39m + 2m2 = 45m + -45m

Combine like terms: 45m + -45m = 0
90 + -39m + 2m2 = 0

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

Divide each side by '2'.
45 + -19.5m + m2 = 0

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -19.5m + -45 + m2 = 0 + -45

Reorder the terms:
45 + -45 + -19.5m + m2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -19.5m + m2 = 0 + -45
-19.5m + m2 = 0 + -45

Combine like terms: 0 + -45 = -45
-19.5m + m2 = -45

The m term is -19.5m.  Take half its coefficient (-9.75).
Square it (95.0625) and add it to both sides.

Add '95.0625' to each side of the equation.
-19.5m + 95.0625 + m2 = -45 + 95.0625

Reorder the terms:
95.0625 + -19.5m + m2 = -45 + 95.0625

Combine like terms: -45 + 95.0625 = 50.0625
95.0625 + -19.5m + m2 = 50.0625

Factor a perfect square on the left side:
(m + -9.75)(m + -9.75) = 50.0625

Calculate the square root of the right side: 7.075485849

Break this problem into two subproblems by setting 
(m + -9.75) equal to 7.075485849 and -7.075485849.

Subproblem 1
m + -9.75 = 7.075485849

Simplifying
m + -9.75 = 7.075485849

Reorder the terms:
-9.75 + m = 7.075485849

Solving
-9.75 + m = 7.075485849

Solving for variable 'm'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + m = 7.075485849 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + m = 7.075485849 + 9.75
m = 7.075485849 + 9.75

Combine like terms: 7.075485849 + 9.75 = 16.825485849
m = 16.825485849

Simplifying
m = 16.825485849

Subproblem 2
m + -9.75 = -7.075485849

Simplifying
m + -9.75 = -7.075485849

Reorder the terms:
-9.75 + m = -7.075485849

Solving
-9.75 + m = -7.075485849

Solving for variable 'm'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + m = -7.075485849 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + m = -7.075485849 + 9.75
m = -7.075485849 + 9.75

Combine like terms: -7.075485849 + 9.75 = 2.674514151
m = 2.674514151

Simplifying
m = 2.674514151

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {16.825485849, 2.674514151}