(5m-1)(m+2)=0

Solution for (5m-1)(m+2)=0 equation:

Simplifying
(5m + -1)(m + 2) = 0

Reorder the terms:
(-1 + 5m)(m + 2) = 0

Reorder the terms:
(-1 + 5m)(2 + m) = 0

Multiply (-1 + 5m) * (2 + m)
(-1(2 + m) + 5m * (2 + m)) = 0
((2 * -1 + m * -1) + 5m * (2 + m)) = 0
((-2 + -1m) + 5m * (2 + m)) = 0
(-2 + -1m + (2 * 5m + m * 5m)) = 0
(-2 + -1m + (10m + 5m2)) = 0

Combine like terms: -1m + 10m = 9m
(-2 + 9m + 5m2) = 0

Solving
-2 + 9m + 5m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-2 + -1m)(1 + -5m) = 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 '(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}