o^2+5o-24=0

Solution for o^2+5o-24=0 equation:

Simplifying
o2 + 5o + -24 = 0

Reorder the terms:
-24 + 5o + o2 = 0

Solving
-24 + 5o + o2 = 0

Solving for variable 'o'.

Factor a trinomial.
(-8 + -1o)(3 + -1o) = 0

Subproblem 1
Set the factor '(-8 + -1o)' equal to zero and attempt to solve:

Simplifying
-8 + -1o = 0

Solving
-8 + -1o = 0

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

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

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

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

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

Simplifying
o = -8
Subproblem 2
Set the factor '(3 + -1o)' equal to zero and attempt to solve:

Simplifying
3 + -1o = 0

Solving
3 + -1o = 0

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

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

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

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

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

Simplifying
o = 3
Solution
o = {-8, 3}