10m^2+9m+2=0

Solution for 10m^2+9m+2=0 equation:

Simplifying
10m2 + 9m + 2 = 0

Reorder the terms:
2 + 9m + 10m2 = 0

Solving
2 + 9m + 10m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(1 + 2m)(2 + 5m) = 0

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

Simplifying
1 + 2m = 0

Solving
1 + 2m = 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 + 2m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2m = 0 + -1
2m = 0 + -1

Combine like terms: 0 + -1 = -1
2m = -1

Divide each side by '2'.
m = -0.5

Simplifying
m = -0.5
Subproblem 2
Set the factor '(2 + 5m)' equal to zero and attempt to solve:

Simplifying
2 + 5m = 0

Solving
2 + 5m = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5m = 0 + -2
5m = 0 + -2

Combine like terms: 0 + -2 = -2
5m = -2

Divide each side by '5'.
m = -0.4

Simplifying
m = -0.4
Solution
m = {-0.5, -0.4}