2m+m(m+10)=180

Solution for 2m+m(m+10)=180 equation:

Simplifying
2m + m(m + 10) = 180

Reorder the terms:
2m + m(10 + m) = 180
2m + (10 * m + m * m) = 180
2m + (10m + m2) = 180

Combine like terms: 2m + 10m = 12m
12m + m2 = 180

Solving
12m + m2 = 180

Solving for variable 'm'.

Reorder the terms:
-180 + 12m + m2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 12m + 180 + m2 = 0 + 180

Reorder the terms:
-180 + 180 + 12m + m2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 12m + m2 = 0 + 180
12m + m2 = 0 + 180

Combine like terms: 0 + 180 = 180
12m + m2 = 180

The m term is 12m.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12m + 36 + m2 = 180 + 36

Reorder the terms:
36 + 12m + m2 = 180 + 36

Combine like terms: 180 + 36 = 216
36 + 12m + m2 = 216

Factor a perfect square on the left side:
(m + 6)(m + 6) = 216

Calculate the square root of the right side: 14.696938457

Break this problem into two subproblems by setting 
(m + 6) equal to 14.696938457 and -14.696938457.

Subproblem 1
m + 6 = 14.696938457

Simplifying
m + 6 = 14.696938457

Reorder the terms:
6 + m = 14.696938457

Solving
6 + m = 14.696938457

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = 14.696938457 + -6

Combine like terms: 6 + -6 = 0
0 + m = 14.696938457 + -6
m = 14.696938457 + -6

Combine like terms: 14.696938457 + -6 = 8.696938457
m = 8.696938457

Simplifying
m = 8.696938457

Subproblem 2
m + 6 = -14.696938457

Simplifying
m + 6 = -14.696938457

Reorder the terms:
6 + m = -14.696938457

Solving
6 + m = -14.696938457

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = -14.696938457 + -6

Combine like terms: 6 + -6 = 0
0 + m = -14.696938457 + -6
m = -14.696938457 + -6

Combine like terms: -14.696938457 + -6 = -20.696938457
m = -20.696938457

Simplifying
m = -20.696938457

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {8.696938457, -20.696938457}