5m^2+7m-138=0

Solution for 5m^2+7m-138=0 equation:

Simplifying
5m2 + 7m + -138 = 0

Reorder the terms:
-138 + 7m + 5m2 = 0

Solving
-138 + 7m + 5m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-6 + -1m)(23 + -5m) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(23 + -5m)' equal to zero and attempt to solve:

Simplifying
23 + -5m = 0

Solving
23 + -5m = 0

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

Add '-23' to each side of the equation.
23 + -23 + -5m = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -5m = 0 + -23
-5m = 0 + -23

Combine like terms: 0 + -23 = -23
-5m = -23

Divide each side by '-5'.
m = 4.6

Simplifying
m = 4.6
Solution
m = {-6, 4.6}