2m^2+14m=-24

Solution for 2m^2+14m=-24 equation:

Simplifying
2m2 + 14m = -24

Reorder the terms:
14m + 2m2 = -24

Solving
14m + 2m2 = -24

Solving for variable 'm'.

Reorder the terms:
24 + 14m + 2m2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 14m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 7m + m2) = 0

Factor a trinomial.
2((4 + m)(3 + 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 '(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
Solution
m = {-4, -3}