m^2+24+10m=0

Solution for m^2+24+10m=0 equation:

Simplifying
m2 + 24 + 10m = 0

Reorder the terms:
24 + 10m + m2 = 0

Solving
24 + 10m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(6 + m)(4 + m) = 0

Subproblem 1
Set the factor '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 0

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

Add '-6' to each side of the equation.
6 + -6 + m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + m = 0 + -6
m = 0 + -6

Combine like terms: 0 + -6 = -6
m = -6

Simplifying
m = -6
Subproblem 2
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
Solution
m = {-6, -4}