(m^2-m)+(2m+m^2)=0

Solution for (m^2-m)+(2m+m^2)=0 equation:

Simplifying
(m2 + -1m) + (2m + m2) = 0

Reorder the terms:
(-1m + m2) + (2m + m2) = 0

Remove parenthesis around (-1m + m2)
-1m + m2 + (2m + m2) = 0

Remove parenthesis around (2m + m2)
-1m + m2 + 2m + m2 = 0

Reorder the terms:
-1m + 2m + m2 + m2 = 0

Combine like terms: -1m + 2m = 1m
1m + m2 + m2 = 0

Combine like terms: m2 + m2 = 2m2
1m + 2m2 = 0

Solving
1m + 2m2 = 0

Solving for variable 'm'.

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

Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(1 + 2m)' equal to zero and attempt to solve:

Simplifying
1 + 2m = 0

Solving
1 + 2m = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2m = 0 + -1
2m = 0 + -1

Combine like terms: 0 + -1 = -1
2m = -1

Divide each side by '2'.
m = -0.5

Simplifying
m = -0.5
Solution
m = {0, -0.5}