(m+3)2m+1=5m+2

Solution for (m+3)2m+1=5m+2 equation:

Simplifying
(m + 3) * 2m + 1 = 5m + 2

Reorder the terms:
(3 + m) * 2m + 1 = 5m + 2

Reorder the terms for easier multiplication:
2m(3 + m) + 1 = 5m + 2
(3 * 2m + m * 2m) + 1 = 5m + 2
(6m + 2m2) + 1 = 5m + 2

Reorder the terms:
1 + 6m + 2m2 = 5m + 2

Reorder the terms:
1 + 6m + 2m2 = 2 + 5m

Solving
1 + 6m + 2m2 = 2 + 5m

Solving for variable 'm'.

Reorder the terms:
1 + -2 + 6m + -5m + 2m2 = 2 + 5m + -2 + -5m

Combine like terms: 1 + -2 = -1
-1 + 6m + -5m + 2m2 = 2 + 5m + -2 + -5m

Combine like terms: 6m + -5m = 1m
-1 + 1m + 2m2 = 2 + 5m + -2 + -5m

Reorder the terms:
-1 + 1m + 2m2 = 2 + -2 + 5m + -5m

Combine like terms: 2 + -2 = 0
-1 + 1m + 2m2 = 0 + 5m + -5m
-1 + 1m + 2m2 = 5m + -5m

Combine like terms: 5m + -5m = 0
-1 + 1m + 2m2 = 0

Factor a trinomial.
(-1 + -1m)(1 + -2m) = 0

Subproblem 1
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
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 = {-1, 0.5}