45m^2-6m-3=0

Solution for 45m^2-6m-3=0 equation:

Simplifying
45m2 + -6m + -3 = 0

Reorder the terms:
-3 + -6m + 45m2 = 0

Solving
-3 + -6m + 45m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -2m + 15m2) = 0

Factor a trinomial.
3((-1 + -5m)(1 + -3m)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -5m)' equal to zero and attempt to solve:

Simplifying
-1 + -5m = 0

Solving
-1 + -5m = 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 + -5m = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5m = 0 + 1
-5m = 0 + 1

Combine like terms: 0 + 1 = 1
-5m = 1

Divide each side by '-5'.
m = -0.2

Simplifying
m = -0.2
Subproblem 2
Set the factor '(1 + -3m)' equal to zero and attempt to solve:

Simplifying
1 + -3m = 0

Solving
1 + -3m = 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 + -3m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3m = 0 + -1
-3m = 0 + -1

Combine like terms: 0 + -1 = -1
-3m = -1

Divide each side by '-3'.
m = 0.3333333333

Simplifying
m = 0.3333333333
Solution
m = {-0.2, 0.3333333333}