0=p^2+2p-24

Solution for 0=p^2+2p-24 equation:

Simplifying
0 = p2 + 2p + -24

Reorder the terms:
0 = -24 + 2p + p2

Solving
0 = -24 + 2p + p2

Solving for variable 'p'.

Combine like terms: 0 + 24 = 24
24 + -2p + -1p2 = -24 + 2p + p2 + 24 + -2p + -1p2

Reorder the terms:
24 + -2p + -1p2 = -24 + 24 + 2p + -2p + p2 + -1p2

Combine like terms: -24 + 24 = 0
24 + -2p + -1p2 = 0 + 2p + -2p + p2 + -1p2
24 + -2p + -1p2 = 2p + -2p + p2 + -1p2

Combine like terms: 2p + -2p = 0
24 + -2p + -1p2 = 0 + p2 + -1p2
24 + -2p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
24 + -2p + -1p2 = 0

Factor a trinomial.
(4 + -1p)(6 + p) = 0

Subproblem 1
Set the factor '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

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

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

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

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

Simplifying
p = 4
Subproblem 2
Set the factor '(6 + p)' equal to zero and attempt to solve:

Simplifying
6 + p = 0

Solving
6 + p = 0

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

Add '-6' to each side of the equation.
6 + -6 + p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + p = 0 + -6
p = 0 + -6

Combine like terms: 0 + -6 = -6
p = -6

Simplifying
p = -6
Solution
p = {4, -6}