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

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

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

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

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

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

Combine like terms: -3m + 30m = 27m
(-6 + 27m + 15m2) = 0

Solving
-6 + 27m + 15m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 9m + 5m2) = 0

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

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

Simplifying
-2 + -1m = 0

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

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

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

Divide each side by '-1'.
m = -2

Simplifying
m = -2
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 = {-2, 0.2}