(m-7)(m+1)=0

Solution for (m-7)(m+1)=0 equation:

Simplifying
(m + -7)(m + 1) = 0

Reorder the terms:
(-7 + m)(m + 1) = 0

Reorder the terms:
(-7 + m)(1 + m) = 0

Multiply (-7 + m) * (1 + m)
(-7(1 + m) + m(1 + m)) = 0
((1 * -7 + m * -7) + m(1 + m)) = 0
((-7 + -7m) + m(1 + m)) = 0
(-7 + -7m + (1 * m + m * m)) = 0
(-7 + -7m + (1m + m2)) = 0

Combine like terms: -7m + 1m = -6m
(-7 + -6m + m2) = 0

Solving
-7 + -6m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-1 + -1m)(7 + -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 '(7 + -1m)' equal to zero and attempt to solve:

Simplifying
7 + -1m = 0

Solving
7 + -1m = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1m = 0 + -7
-1m = 0 + -7

Combine like terms: 0 + -7 = -7
-1m = -7

Divide each side by '-1'.
m = 7

Simplifying
m = 7
Solution
m = {-1, 7}