6m^2-66m+180=0

Solution for 6m^2-66m+180=0 equation:

Simplifying
6m2 + -66m + 180 = 0

Reorder the terms:
180 + -66m + 6m2 = 0

Solving
180 + -66m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6'.
6(30 + -11m + m2) = 0

Factor a trinomial.
6((5 + -1m)(6 + -1m)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + -1m)' equal to zero and attempt to solve:

Simplifying
5 + -1m = 0

Solving
5 + -1m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
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 = {5, 6}