6m^2-42m=-36

Solution for 6m^2-42m=-36 equation:

Simplifying
6m2 + -42m = -36

Reorder the terms:
-42m + 6m2 = -36

Solving
-42m + 6m2 = -36

Solving for variable 'm'.

Reorder the terms:
36 + -42m + 6m2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -42m + 6m2 = 0

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

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

Ignore the factor 6.
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 '(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 = {1, 6}