9m^2+3m-6=0

Solution for 9m^2+3m-6=0 equation:

Simplifying
9m2 + 3m + -6 = 0

Reorder the terms:
-6 + 3m + 9m2 = 0

Solving
-6 + 3m + 9m2 = 0

Solving for variable 'm'.

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

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

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

Simplifying
-1 + -1m = 0

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

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

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

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

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

Simplifying
2 + -3m = 0

Solving
2 + -3m = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3m = 0 + -2
-3m = 0 + -2

Combine like terms: 0 + -2 = -2
-3m = -2

Divide each side by '-3'.
m = 0.6666666667

Simplifying
m = 0.6666666667
Solution
m = {-1, 0.6666666667}