24m^2-126m-111=-3

Solution for 24m^2-126m-111=-3 equation:

Simplifying
24m2 + -126m + -111 = -3

Reorder the terms:
-111 + -126m + 24m2 = -3

Solving
-111 + -126m + 24m2 = -3

Solving for variable 'm'.

Reorder the terms:
-111 + 3 + -126m + 24m2 = -3 + 3

Combine like terms: -111 + 3 = -108
-108 + -126m + 24m2 = -3 + 3

Combine like terms: -3 + 3 = 0
-108 + -126m + 24m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + -21m + 4m2) = 0

Factor a trinomial.
6((-3 + -4m)(6 + -1m)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 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 + -1m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m = 0 + -6
-1m = 0 + -6

Combine like terms: 0 + -6 = -6
-1m = -6

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Solution
m = {-0.75, 6}