m(3m+1)=3m+1

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

Simplifying
m(3m + 1) = 3m + 1

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

Reorder the terms:
1m + 3m2 = 1 + 3m

Solving
1m + 3m2 = 1 + 3m

Solving for variable 'm'.

Reorder the terms:
-1 + 1m + -3m + 3m2 = 1 + 3m + -1 + -3m

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

Reorder the terms:
-1 + -2m + 3m2 = 1 + -1 + 3m + -3m

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

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

Factor a trinomial.
(-1 + -3m)(1 + -1m) = 0

Subproblem 1
Set the factor '(-1 + -3m)' equal to zero and attempt to solve:

Simplifying
-1 + -3m = 0

Solving
-1 + -3m = 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 + -3m = 0 + 1

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

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

Divide each side by '-3'.
m = -0.3333333333

Simplifying
m = -0.3333333333
Subproblem 2
Set the factor '(1 + -1m)' equal to zero and attempt to solve:

Simplifying
1 + -1m = 0

Solving
1 + -1m = 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 + -1m = 0 + -1

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

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

Divide each side by '-1'.
m = 1

Simplifying
m = 1
Solution
m = {-0.3333333333, 1}