(m+4)(m-5)+8=0

Solution for (m+4)(m-5)+8=0 equation:

Simplifying
(m + 4)(m + -5) + 8 = 0

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

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

Multiply (4 + m) * (-5 + m)
(4(-5 + m) + m(-5 + m)) + 8 = 0
((-5 * 4 + m * 4) + m(-5 + m)) + 8 = 0
((-20 + 4m) + m(-5 + m)) + 8 = 0
(-20 + 4m + (-5 * m + m * m)) + 8 = 0
(-20 + 4m + (-5m + m2)) + 8 = 0

Combine like terms: 4m + -5m = -1m
(-20 + -1m + m2) + 8 = 0

Reorder the terms:
-20 + 8 + -1m + m2 = 0

Combine like terms: -20 + 8 = -12
-12 + -1m + m2 = 0

Solving
-12 + -1m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3 + -1m)(4 + -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 '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Solution
m = {-3, 4}