(m-8)(m+1)=0

Solution for (m-8)(m+1)=0 equation:

Simplifying
(m + -8)(m + 1) = 0

Reorder the terms:
(-8 + m)(m + 1) = 0

Reorder the terms:
(-8 + m)(1 + m) = 0

Multiply (-8 + m) * (1 + m)
(-8(1 + m) + m(1 + m)) = 0
((1 * -8 + m * -8) + m(1 + m)) = 0
((-8 + -8m) + m(1 + m)) = 0
(-8 + -8m + (1 * m + m * m)) = 0
(-8 + -8m + (1m + m2)) = 0

Combine like terms: -8m + 1m = -7m
(-8 + -7m + m2) = 0

Solving
-8 + -7m + m2 = 0

Solving for variable 'm'.

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

Subproblem 1
Set the factor '(-1 + -1m)' equal to zero and attempt to solve:

Simplifying
-1 + -1m = 0

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

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

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

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

Simplifying
m = -1
Subproblem 2
Set the factor '(8 + -1m)' equal to zero and attempt to solve:

Simplifying
8 + -1m = 0

Solving
8 + -1m = 0

Move all terms containing m to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1m = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1m = 0 + -8
-1m = 0 + -8

Combine like terms: 0 + -8 = -8
-1m = -8

Divide each side by '-1'.
m = 8

Simplifying
m = 8
Solution
m = {-1, 8}