6m^2-42m=-72

Solution for 6m^2-42m=-72 equation:

Simplifying
6m2 + -42m = -72

Reorder the terms:
-42m + 6m2 = -72

Solving
-42m + 6m2 = -72

Solving for variable 'm'.

Reorder the terms:
72 + -42m + 6m2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -42m + 6m2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7m + m2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Solution
m = {3, 4}