3m^2=6m+9

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

Simplifying
3m2 = 6m + 9

Reorder the terms:
3m2 = 9 + 6m

Solving
3m2 = 9 + 6m

Solving for variable 'm'.

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

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

Combine like terms: 9 + -9 = 0
-9 + -6m + 3m2 = 0 + 6m + -6m
-9 + -6m + 3m2 = 6m + -6m

Combine like terms: 6m + -6m = 0
-9 + -6m + 3m2 = 0

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

Factor a trinomial.
3((-1 + -1m)(3 + -1m)) = 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 '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 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 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {-1, 3}