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

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

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

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

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

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

Combine like terms: -5m + 2m = -3m
3(-10 + -3m + m2) = 0
(-10 * 3 + -3m * 3 + m2 * 3) = 0
(-30 + -9m + 3m2) = 0

Solving
-30 + -9m + 3m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3m + m2) = 0

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

Ignore the factor 3.
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 + -1m)' equal to zero and attempt to solve:

Simplifying
5 + -1m = 0

Solving
5 + -1m = 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 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Solution
m = {-2, 5}