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

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

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

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

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

Multiply (-6 + 5m) * (1 + 3m)
(-6(1 + 3m) + 5m * (1 + 3m)) = 0
((1 * -6 + 3m * -6) + 5m * (1 + 3m)) = 0
((-6 + -18m) + 5m * (1 + 3m)) = 0
(-6 + -18m + (1 * 5m + 3m * 5m)) = 0
(-6 + -18m + (5m + 15m2)) = 0

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

Solving
-6 + -13m + 15m2 = 0

Solving for variable 'm'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -5m)' equal to zero and attempt to solve:

Simplifying
6 + -5m = 0

Solving
6 + -5m = 0

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

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

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

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

Divide each side by '-5'.
m = 1.2

Simplifying
m = 1.2
Solution
m = {-0.3333333333, 1.2}