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

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

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

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

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

Multiply (3 + m) * (-2 + 5m)
(3(-2 + 5m) + m(-2 + 5m)) = 0
((-2 * 3 + 5m * 3) + m(-2 + 5m)) = 0
((-6 + 15m) + m(-2 + 5m)) = 0
(-6 + 15m + (-2 * m + 5m * m)) = 0
(-6 + 15m + (-2m + 5m2)) = 0

Combine like terms: 15m + -2m = 13m
(-6 + 13m + 5m2) = 0

Solving
-6 + 13m + 5m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -1m)(2 + -5m) = 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 '(2 + -5m)' equal to zero and attempt to solve:

Simplifying
2 + -5m = 0

Solving
2 + -5m = 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 + -5m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5m = 0 + -2
-5m = 0 + -2

Combine like terms: 0 + -2 = -2
-5m = -2

Divide each side by '-5'.
m = 0.4

Simplifying
m = 0.4
Solution
m = {-3, 0.4}