m(m+2)=24-3m

Solution for m(m+2)=24-3m equation:

Simplifying
m(m + 2) = 24 + -3m

Reorder the terms:
m(2 + m) = 24 + -3m
(2 * m + m * m) = 24 + -3m
(2m + m2) = 24 + -3m

Solving
2m + m2 = 24 + -3m

Solving for variable 'm'.

Reorder the terms:
-24 + 2m + 3m + m2 = 24 + -3m + -24 + 3m

Combine like terms: 2m + 3m = 5m
-24 + 5m + m2 = 24 + -3m + -24 + 3m

Reorder the terms:
-24 + 5m + m2 = 24 + -24 + -3m + 3m

Combine like terms: 24 + -24 = 0
-24 + 5m + m2 = 0 + -3m + 3m
-24 + 5m + m2 = -3m + 3m

Combine like terms: -3m + 3m = 0
-24 + 5m + m2 = 0

Factor a trinomial.
(-8 + -1m)(3 + -1m) = 0

Subproblem 1
Set the factor '(-8 + -1m)' equal to zero and attempt to solve:

Simplifying
-8 + -1m = 0

Solving
-8 + -1m = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1m = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1m = 0 + 8
-1m = 0 + 8

Combine like terms: 0 + 8 = 8
-1m = 8

Divide each side by '-1'.
m = -8

Simplifying
m = -8
Subproblem 2
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

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

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

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

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {-8, 3}