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

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

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

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

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

Multiply (-5 + 6m) * (3 + m)
(-5(3 + m) + 6m * (3 + m)) = 0
((3 * -5 + m * -5) + 6m * (3 + m)) = 0
((-15 + -5m) + 6m * (3 + m)) = 0
(-15 + -5m + (3 * 6m + m * 6m)) = 0
(-15 + -5m + (18m + 6m2)) = 0

Combine like terms: -5m + 18m = 13m
(-15 + 13m + 6m2) = 0

Solving
-15 + 13m + 6m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -1m)(5 + -6m) = 0

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

Simplifying
-3 + -1m = 0

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

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

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

Divide each side by '-1'.
m = -3

Simplifying
m = -3
Subproblem 2
Set the factor '(5 + -6m)' equal to zero and attempt to solve:

Simplifying
5 + -6m = 0

Solving
5 + -6m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6m = 0 + -5
-6m = 0 + -5

Combine like terms: 0 + -5 = -5
-6m = -5

Divide each side by '-6'.
m = 0.8333333333

Simplifying
m = 0.8333333333
Solution
m = {-3, 0.8333333333}