10m^2-3m-27=0

Solution for 10m^2-3m-27=0 equation:

Simplifying
10m2 + -3m + -27 = 0

Reorder the terms:
-27 + -3m + 10m2 = 0

Solving
-27 + -3m + 10m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -2m)(9 + -5m) = 0

Subproblem 1
Set the factor '(-3 + -2m)' equal to zero and attempt to solve:

Simplifying
-3 + -2m = 0

Solving
-3 + -2m = 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 + -2m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2m = 0 + 3
-2m = 0 + 3

Combine like terms: 0 + 3 = 3
-2m = 3

Divide each side by '-2'.
m = -1.5

Simplifying
m = -1.5
Subproblem 2
Set the factor '(9 + -5m)' equal to zero and attempt to solve:

Simplifying
9 + -5m = 0

Solving
9 + -5m = 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 + -5m = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5m = 0 + -9
-5m = 0 + -9

Combine like terms: 0 + -9 = -9
-5m = -9

Divide each side by '-5'.
m = 1.8

Simplifying
m = 1.8
Solution
m = {-1.5, 1.8}