24m^2-6m-9=0

Solution for 24m^2-6m-9=0 equation:

Simplifying
24m2 + -6m + -9 = 0

Reorder the terms:
-9 + -6m + 24m2 = 0

Solving
-9 + -6m + 24m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -2m + 8m2) = 0

Factor a trinomial.
3((-1 + -2m)(3 + -4m)) = 0

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

Simplifying
-1 + -2m = 0

Solving
-1 + -2m = 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 + -2m = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2m = 0 + 1
-2m = 0 + 1

Combine like terms: 0 + 1 = 1
-2m = 1

Divide each side by '-2'.
m = -0.5

Simplifying
m = -0.5
Subproblem 2
Set the factor '(3 + -4m)' equal to zero and attempt to solve:

Simplifying
3 + -4m = 0

Solving
3 + -4m = 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 + -4m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4m = 0 + -3
-4m = 0 + -3

Combine like terms: 0 + -3 = -3
-4m = -3

Divide each side by '-4'.
m = 0.75

Simplifying
m = 0.75
Solution
m = {-0.5, 0.75}