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

Solution for 8(m-2)(m+5)=0 equation:

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

Reorder the terms:
8(-2 + m)(m + 5) = 0

Reorder the terms:
8(-2 + m)(5 + m) = 0

Multiply (-2 + m) * (5 + m)
8(-2(5 + m) + m(5 + m)) = 0
8((5 * -2 + m * -2) + m(5 + m)) = 0
8((-10 + -2m) + m(5 + m)) = 0
8(-10 + -2m + (5 * m + m * m)) = 0
8(-10 + -2m + (5m + m2)) = 0

Combine like terms: -2m + 5m = 3m
8(-10 + 3m + m2) = 0
(-10 * 8 + 3m * 8 + m2 * 8) = 0
(-80 + 24m + 8m2) = 0

Solving
-80 + 24m + 8m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-10 + 3m + m2) = 0

Factor a trinomial.
8((-5 + -1m)(2 + -1m)) = 0

Ignore the factor 8.
Subproblem 1
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
Subproblem 2
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
Solution
m = {-5, 2}