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

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

Simplifying
(4 + m)(2 + -1m + 3m) = 0

Combine like terms: -1m + 3m = 2m
(4 + m)(2 + 2m) = 0

Multiply (4 + m) * (2 + 2m)
(4(2 + 2m) + m(2 + 2m)) = 0
((2 * 4 + 2m * 4) + m(2 + 2m)) = 0
((8 + 8m) + m(2 + 2m)) = 0
(8 + 8m + (2 * m + 2m * m)) = 0
(8 + 8m + (2m + 2m2)) = 0

Combine like terms: 8m + 2m = 10m
(8 + 10m + 2m2) = 0

Solving
8 + 10m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5m + m2) = 0

Factor a trinomial.
2((4 + m)(1 + m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + m)' equal to zero and attempt to solve:

Simplifying
4 + m = 0

Solving
4 + m = 0

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

Add '-4' to each side of the equation.
4 + -4 + m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + m = 0 + -4
m = 0 + -4

Combine like terms: 0 + -4 = -4
m = -4

Simplifying
m = -4
Subproblem 2
Set the factor '(1 + m)' equal to zero and attempt to solve:

Simplifying
1 + m = 0

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

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

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

Simplifying
m = -1
Solution
m = {-4, -1}