2m^2+3m-54=0

Solution for 2m^2+3m-54=0 equation:

Simplifying
2m2 + 3m + -54 = 0

Reorder the terms:
-54 + 3m + 2m2 = 0

Solving
-54 + 3m + 2m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-6 + -1m)(9 + -2m) = 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 '(9 + -2m)' equal to zero and attempt to solve:

Simplifying
9 + -2m = 0

Solving
9 + -2m = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2m = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2m = 0 + -9
-2m = 0 + -9

Combine like terms: 0 + -9 = -9
-2m = -9

Divide each side by '-2'.
m = 4.5

Simplifying
m = 4.5
Solution
m = {-6, 4.5}