(3+m)(2m+4)=

Solution for (3+m)(2m+4)= equation:

Simplifying
(3 + m)(2m + 4) = 0

Reorder the terms:
(3 + m)(4 + 2m) = 0

Multiply (3 + m) * (4 + 2m)
(3(4 + 2m) + m(4 + 2m)) = 0
((4 * 3 + 2m * 3) + m(4 + 2m)) = 0
((12 + 6m) + m(4 + 2m)) = 0
(12 + 6m + (4 * m + 2m * m)) = 0
(12 + 6m + (4m + 2m2)) = 0

Combine like terms: 6m + 4m = 10m
(12 + 10m + 2m2) = 0

Solving
12 + 10m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5m + m2) = 0

Factor a trinomial.
2((3 + m)(2 + m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + m)' equal to zero and attempt to solve:

Simplifying
3 + m = 0

Solving
3 + m = 0

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

Add '-3' to each side of the equation.
3 + -3 + m = 0 + -3

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

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

Simplifying
m = -3
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 0

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

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

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

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

Simplifying
m = -2
Solution
m = {-3, -2}