(3m-5)(m+2)=0

Solution for (3m-5)(m+2)=0 equation:

Simplifying
(3m + -5)(m + 2) = 0

Reorder the terms:
(-5 + 3m)(m + 2) = 0

Reorder the terms:
(-5 + 3m)(2 + m) = 0

Multiply (-5 + 3m) * (2 + m)
(-5(2 + m) + 3m * (2 + m)) = 0
((2 * -5 + m * -5) + 3m * (2 + m)) = 0
((-10 + -5m) + 3m * (2 + m)) = 0
(-10 + -5m + (2 * 3m + m * 3m)) = 0
(-10 + -5m + (6m + 3m2)) = 0

Combine like terms: -5m + 6m = 1m
(-10 + 1m + 3m2) = 0

Solving
-10 + 1m + 3m2 = 0

Solving for variable 'm'.

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

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 '(5 + -3m)' equal to zero and attempt to solve:

Simplifying
5 + -3m = 0

Solving
5 + -3m = 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 + -3m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3m = 0 + -5
-3m = 0 + -5

Combine like terms: 0 + -5 = -5
-3m = -5

Divide each side by '-3'.
m = 1.666666667

Simplifying
m = 1.666666667
Solution
m = {-2, 1.666666667}