(m+5)(m-7)=-20

Solution for (m+5)(m-7)=-20 equation:

Simplifying
(m + 5)(m + -7) = -20

Reorder the terms:
(5 + m)(m + -7) = -20

Reorder the terms:
(5 + m)(-7 + m) = -20

Multiply (5 + m) * (-7 + m)
(5(-7 + m) + m(-7 + m)) = -20
((-7 * 5 + m * 5) + m(-7 + m)) = -20
((-35 + 5m) + m(-7 + m)) = -20
(-35 + 5m + (-7 * m + m * m)) = -20
(-35 + 5m + (-7m + m2)) = -20

Combine like terms: 5m + -7m = -2m
(-35 + -2m + m2) = -20

Solving
-35 + -2m + m2 = -20

Solving for variable 'm'.

Reorder the terms:
-35 + 20 + -2m + m2 = -20 + 20

Combine like terms: -35 + 20 = -15
-15 + -2m + m2 = -20 + 20

Combine like terms: -20 + 20 = 0
-15 + -2m + m2 = 0

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

Subproblem 1
Set the factor '(-3 + -1m)' equal to zero and attempt to solve:

Simplifying
-3 + -1m = 0

Solving
-3 + -1m = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1m = 0 + 3
-1m = 0 + 3

Combine like terms: 0 + 3 = 3
-1m = 3

Divide each side by '-1'.
m = -3

Simplifying
m = -3
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 = {-3, 5}