(5m-1)(6m+3)=0

Solution for (5m-1)(6m+3)=0 equation:

Simplifying
(5m + -1)(6m + 3) = 0

Reorder the terms:
(-1 + 5m)(6m + 3) = 0

Reorder the terms:
(-1 + 5m)(3 + 6m) = 0

Multiply (-1 + 5m) * (3 + 6m)
(-1(3 + 6m) + 5m * (3 + 6m)) = 0
((3 * -1 + 6m * -1) + 5m * (3 + 6m)) = 0
((-3 + -6m) + 5m * (3 + 6m)) = 0
(-3 + -6m + (3 * 5m + 6m * 5m)) = 0
(-3 + -6m + (15m + 30m2)) = 0

Combine like terms: -6m + 15m = 9m
(-3 + 9m + 30m2) = 0

Solving
-3 + 9m + 30m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 3m + 10m2) = 0

Factor a trinomial.
3((-1 + -2m)(1 + -5m)) = 0

Ignore the factor 3.
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 '(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
Solution
m = {-0.5, 0.2}