2m(m+1)=3m

Solution for 2m(m+1)=3m equation:

Simplifying
2m(m + 1) = 3m

Reorder the terms:
2m(1 + m) = 3m
(1 * 2m + m * 2m) = 3m
(2m + 2m2) = 3m

Solving
2m + 2m2 = 3m

Solving for variable 'm'.

Reorder the terms:
2m + -3m + 2m2 = 3m + -3m

Combine like terms: 2m + -3m = -1m
-1m + 2m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
-1m + 2m2 = 0

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}