(m+8)(m-3)+24=0

Solution for (m+8)(m-3)+24=0 equation:

Simplifying
(m + 8)(m + -3) + 24 = 0

Reorder the terms:
(8 + m)(m + -3) + 24 = 0

Reorder the terms:
(8 + m)(-3 + m) + 24 = 0

Multiply (8 + m) * (-3 + m)
(8(-3 + m) + m(-3 + m)) + 24 = 0
((-3 * 8 + m * 8) + m(-3 + m)) + 24 = 0
((-24 + 8m) + m(-3 + m)) + 24 = 0
(-24 + 8m + (-3 * m + m * m)) + 24 = 0
(-24 + 8m + (-3m + m2)) + 24 = 0

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

Reorder the terms:
-24 + 24 + 5m + m2 = 0

Combine like terms: -24 + 24 = 0
0 + 5m + m2 = 0
5m + m2 = 0

Solving
5m + m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm'.
m(5 + m) = 0

Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(5 + m)' equal to zero and attempt to solve:

Simplifying
5 + m = 0

Solving
5 + m = 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 + m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + m = 0 + -5
m = 0 + -5

Combine like terms: 0 + -5 = -5
m = -5

Simplifying
m = -5
Solution
m = {0, -5}